Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry]
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Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry], 2016, Volume 12, Number 2, Pages 113–133
DOI: https://doi.org/10.15407/mag12.02.113 (Mi jmag648) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On stabilization problem for nonlinear systems with power principal part

M. O. Bebiya, V. I. Korobov

Department of Mathematics and Informatics, V.N. Karazin Kharkiv National University, 4 Svobody Sq., Kharkiv 61022, Ukraine
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DOI: https://doi.org/10.15407/mag12.02.113
Abstract: In the present paper, the stabilization problem for the uncontrollable with respect to the first approximation nonlinear system with power principal part is solved. A class of stabilizing controls for the nonlinear approximation of this system is constructed by using the Lyapunov function method. It is proved that the same controls solve the stabilization problem for the original nonlinear system. An ellipsoidal approximation of the domain of attraction to the origin is given.
Key words and phrases: nonlinear stabilization, nonlinear systems, Lyapunov function method, nonlinear approximation.
Received: 05.06.2015
Revised: 21.10.2015
Bibliographic databases:
Document Type: Article
MSC: 93C10, 93D15, 93D30
Language: English
Citation: M. O. Bebiya, V. I. Korobov, “On stabilization problem for nonlinear systems with power principal part”, Zh. Mat. Fiz. Anal. Geom., 12:2 (2016), 113–133
Citation in format AMSBIB
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\by M.~O.~Bebiya, V.~I.~Korobov
\paper On stabilization problem for nonlinear systems with power principal part
\jour Zh. Mat. Fiz. Anal. Geom.
\yr 2016
\vol 12
\issue 2
\pages 113--133
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