of 71
8/18/2019 Nonlinear Controls theory
1/71
8/18/2019 Nonlinear Controls theory
2/71
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
8/18/2019 Nonlinear Controls theory
3/71
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
8/18/2019 Nonlinear Controls theory
4/71
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
8/18/2019 Nonlinear Controls theory
5/71
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
8/18/2019 Nonlinear Controls theory
6/71
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
8/18/2019 Nonlinear Controls theory
7/71
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
8/18/2019 Nonlinear Controls theory
8/71
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
8/18/2019 Nonlinear Controls theory
9/71
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
8/18/2019 Nonlinear Controls theory
10/71
8/18/2019 Nonlinear Controls theory
11/71
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
8/18/2019 Nonlinear Controls theory
12/71
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
8/18/2019 Nonlinear Controls theory
13/71
8/18/2019 Nonlinear Controls theory
14/71
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
8/18/2019 Nonlinear Controls theory
15/71
8/18/2019 Nonlinear Controls theory
16/71
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
8/18/2019 Nonlinear Controls theory
17/71
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
8/18/2019 Nonlinear Controls theory
18/71
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
8/18/2019 Nonlinear Controls theory
19/71
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
8/18/2019 Nonlinear Controls theory
20/71
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
8/18/2019 Nonlinear Controls theory
21/71
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
catcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatca
tcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatc
atcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcatcat
8/18/