Solutions to Lyapunov stability problems of sets: nonlinear systems with differentiable motions

Ljubomir T. Grujic

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

Abstract:

Time-invariant nonlinear systems with differentiable motions are considered. The algorithmic necessary and sufficient conditions are established in various forms for one-shot construction of a Lyapunov function, for asymptotic stability of a compact invariant set and for the exact determination of the asymptotic stability domain of the invariant set.

The classical conditions are expressed in terms of existence of a system Lyapunov functions. The conditions of theorems presented herein are expressed via properties of the solution ? to ? ? = - p , or of the solution ? to ? ? = - ( 1 - ? ) p , for arbitrarily selected p ? P ( S ; f ) or p ? P 1 ( S ; f ) , where families P ( S ; f ) and P 1 ( S ; f ) are well defined. The equation ? ? = - p , or its equivalent ? ? = - ( 1 - ? ) p , should be solved only for one selection of the function p .

Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:501053

DOI: 10.1155/S0161171294000141

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