# Stabilization of some class of nonlinear systems that are uncontrollable the first approximation

 Title Stabilization of some class of nonlinear systems that are uncontrollable the first approximation Publication Type Journal Article Year of Publication 2014 Authors Korobov, VI, Bebiya, MO Abbreviated Key Title Dopov. Nac. akad. nauk Ukr. DOI 10.15407/dopovidi2014.02.020 Issue 2 Section Mathematics Pagination 20-25 Date Published 2/2014 Language Russian Abstract The problem of stabilization for systems of the form $\dot x_{1}=u$, $\dot x_{i}=x_{i-1}+f_{i-1}(t,x_{1},\ldots,x_{n})$, $\dot x_{n}=x^{2k+1}_{n-1}+f_{n-1}(t,x_{1},\ldots,x_{n})$, $i=\overline{2,n-1}$, that are uncontrollable in the first approximation is considered. The sufficient condition of existence of a quadratic Lyapunov function is obtained, and a method of construction of the Lyapunov function and the stabilizing control is described. Keywords nonlinear systems, stabilization, uncontrol
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