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

TitleStabilization of some class of nonlinear systems that are uncontrollable the first approximation
Publication TypeJournal Article
Year of Publication2014
AuthorsKorobov, VI, Bebiya, MO
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2014.02.020
Issue2
SectionMathematics
Pagination20-25
Date Published2/2014
LanguageRussian
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.
Keywordsnonlinear systems, stabilization, uncontrol
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