Finite-Time Stability of Impulsive Switched Systems

This article studies finite-time stability (FTS) of impulsive switched systems. Some sufficient criteria based on multiple Lyapunov functions coupled with dwell time condition are derived for ensuring the FTS property. It shows that when the mode governing continuous dynamic is finite-time stable but the discrete dynamic involves destabilizing impulses, the FTS can be guaranteed if the impulses can be effectively restrained by dwell time condition. Conversely, when the mode governing continuous dynamic is not finite-time stable but the discrete dynamic involves stabilizing impulses, the system can be successfully stabilized in FTS sense if the impulses are applied frequently. Moreover, when impulsive switched systems consist of stable and unstable modes, the FTS can also be ensured if there is a tradeoff among the activating time of unstable modes, impulsive dynamics, and initial condition. Finally, two examples are proposed to illustrate the efficiency of theoretical results.