International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 3, Pages 587-596

Solutions to Lyapunov stability problems: nonlinear systems with continuous motions

Ljubomir T. Grujić

Faculty of Mechanical Engineering, University in Belgrade, P.O. Box 174, Belgrade 11000, Serbia

Received 23 January 1991; Revised 27 May 1992

Copyright © 1994 Ljubomir T. Grujić. 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.


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.