Journal of Applied Mathematics and Mechanics (about journal) Journal of Applied
Mathematics and Mechanics

Russian Academy of Sciences
 Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
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IssuesArchive of Issues2011-3pp.317-322

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A.M. Kovalev, "Invariance and asymptotic stability," J. Appl. Math. Mech. 75 (3), 317-322 (2011)
Year 2011 Volume 75 Issue 3 Pages 317-322
Title Invariance and asymptotic stability
Author(s) A.M. Kovalev (Donetsk, Ukraine, kovalev@iamm.ac.donetsk.ua)
Abstract The stability of the zero solution of an autonomous non-linear system is considered. The problem of finding the variables in relation to which the solution is asymptotically stable if the Lyapunov function with a sign-definite derivative is known, is formulated and solved. The maximality of the set in relation to which the solution is asymptotically stable is established. The investigation is based on the method of auxiliary functions and clarifies the relation between the properties of invariance and the asymptotic stability of dynamical systems. The constructiveness of the results obtained is demonstrated by an example.
Received 16 October 2010
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