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 Mat. Fiz. Anal. Geom., 2005, Volume 12, Number 1, Pages 3–24 (Mi jmag170)

On the stability of solutions of systems ordinary quadratic differential equations on cone

S. A. Volkova

Ukrainian State University of Chemical Engineering

Abstract: The new sufficient conditions of a conditional stability of the trivial solution of a system of the ordinary quadratic differential equations are obtained. For the homogeneous system a domains of unlocal stability are also indicated (it will be cones). Then this domain is used for design of piecewise linear (discontinuous) control lawes on output for a bilinear control system of any order. Thus a system closed by such discontinuous feed-back becomes globally stable in the Lyapunuv sense for all the state space. The examples are given.

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Bibliographic databases:
MSC: 93B05, 93B27

Citation: S. A. Volkova, “On the stability of solutions of systems ordinary quadratic differential equations on cone”, Mat. Fiz. Anal. Geom., 12:1 (2005), 3–24

Citation in format AMSBIB
\Bibitem{Vol05} \by S.~A.~Volkova \paper On the stability of solutions of systems ordinary quadratic differential equations on cone \jour Mat. Fiz. Anal. Geom. \yr 2005 \vol 12 \issue 1 \pages 3--24 \mathnet{http://mi.mathnet.ru/jmag170} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2135423} \zmath{https://zbmath.org/?q=an:1080.34042}