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Solutions to Lyapunov stability problems: nonlinear systems with continuous motions

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  • Ljubomir T. Grujic

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.

Suggested Citation

  • Ljubomir T. Grujic, 1994. "Solutions to Lyapunov stability problems: nonlinear systems with continuous motions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 17, pages 1-10, January.
    • Handle: RePEc:hin:jijmms:570126
    DOI: 10.1155/S0161171294000839
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