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

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  • Ljubomir T. Grujic

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 .

Suggested Citation

  • Ljubomir T. Grujic, 1994. "Solutions to Lyapunov stability problems of sets: nonlinear systems with differentiable motions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 17, pages 1-10, January.
    • Handle: RePEc:hin:jijmms:501053
    DOI: 10.1155/S0161171294000141
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