A unified approach for stability analysis of impulsive hybrid systems

We present a unified approach for the stability analysis of impulsive hybrid systems. The approach is composed of two key steps. The first step is to group a number of modes of the hybrid system together with the corresponding intervals and reset maps as units. This can be done by analyzing the discrete property of an impulsive hybrid system. The second step is to find an operation to combine each unit together. We show that the system is stable if the Lyapunov function is non-increasing along each unit of the system. In particular, we use the approach to analyze the stability of impulsive differential systems, sampled-data control systems and impulsive switched systems.