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
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 , or of the solution to , for arbitrarily selected or , where families and are well defined. The equation , or its equivalent , should be solved only for one selection of the function .
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