Towards a converse Lyapunov stability theory of hybrid impulsive and switching systems

The converse Lyapunov stability problem is proposed for a special class of hybrid systems, hybrid impulsive and switching systems (HISS). The necessary condition is constructed,under which the HISS is proved to be uniformly asymptotically stable with respect to its equilibrium in the state space. The construction method for Lyapunov functions presented in this paper is different from the other literature. It helps to solve the Lyapunov function construction problem in the process of stability analysis in hybrid dynamical systems (HDS).