Solutions to Lyapunov stability problems: nonlinear systems with continuous motions

Grujic, Ljubomir T.

doi:https://doi.org/10.1155/S0161171294000839

International Journal of Mathematics and Mathematical Sciences

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Volume 17 | Article ID 570126 | https://doi.org/10.1155/S0161171294000839

Solutions to Lyapunov stability problems: nonlinear systems with continuous motions

Ljubomir T. Grujic¹

Received23 Jan 1991

Revised27 May 1992

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.

Copyright

Copyright © 1994 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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