Solutions to Lyapunov stability problems: nonlinear systems with continuous motions

Abstract

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.

Keywords

• stability
• Lyapunov method
• Lyapunov functions
• nonlinear systems
• dynamical systems.