A Continuous Lyapunov Function for Periodic Orbits Based on Poincaré Map

Abstract

This paper presents a continuous Lyapunov function for asymptotically stable periodic orbits of nonlinear systems based on Poincaré map. The function is constructed from a Lyapunov function for discrete-time dynamics on a local section by using the times required for the state to cross the section when it is propagated forward and backward in time.