Solutions to Lyapunov stability problems: nonlinear systems with continuous motions

Ljubomir T. Grujic

International Journal of Mathematics and Mathematical Sciences, 1994, vol. 17, 1-10

Abstract:

The necessary and sufficient conditions for accurate construction of a Lyapunov function and the necessary and sufficient conditions for a set to be the asymptotic stability domain are algorithmically solved for a nonlinear dynamical system with continuous motions. The conditions are established by utilizing properties of o-uniquely bounded sets, which are explained in the paper. They allow arbitrary selection of an o-uniquely bounded set to generate a Lyapunov function.

Simple examples illustrate the theory and its applications.

Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:570126

DOI: 10.1155/S0161171294000839

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