International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1994 / Article

Open Access

Volume 17 |Article ID 501053 | https://doi.org/10.1155/S0161171294000141

Ljubomir T. Grujic, "Solutions to Lyapunov stability problems of sets: nonlinear systems with differentiable motions", International Journal of Mathematics and Mathematical Sciences, vol. 17, Article ID 501053, 10 pages, 1994. https://doi.org/10.1155/S0161171294000141

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

Received23 Jan 1991
Revised28 Apr 1993

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?P1(S;f), where families P(S;f) and P1(S;f) are well defined. The equation ??=-p, or its equivalent ??=-(1-?)p, should be solved only for one selection of the function p.

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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