Ukrainian Mathematical Bulletin
Volume 2, Issue 1, 2005 pp. 77-86.
Investigation of Stability by Using Lyapunov Functions of Fixed SignAuthors: Aleksander O. Ignatyev
Author institution: Institute of Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, 74 Rosa Luxemburg St., Donetsk 83114, Ukraine
Summary: We consider a nonautonomous system of ordinary differential equations admitting the trivial solution for which there exists a nonnegative Lyapunov function whose derivative is nonpositive due to the properties of the system. It is assumed that the trivial solution of the system is uniformly asymptotically stable in the set, where the Lyapunov function turns into zero. We prove theorems on the uniform stability and uniform asymptotic stability and present an example illustrating the proposed approach.
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