Exponential stability of nonlinear switched systems with hybrid delayed impulses

Abstract

AbstractThis article addresses the exponential stability problem of switched systems with hybrid delayed impulses that depend on both current states and historical states. Some sufficient conditions for exponential stability based on Lyapunov functions are obtained. In particular, the potential stabilizing and destabilizing effects of time delays in impulses are investigated. It is shown that when continuous dynamics are stable, the primal stabilizing impulses may destabilize the system if there exist delays in the impulses. Interestingly, under certain conditions, such delayed impulses cannot destroy the stability of the whole system for all impulsive time sequences with arbitrarily bounded impulsive intervals, and the sizes of the delays in the impulses can theoretically be arbitrarily finite. Finally, to illustrate the validity of the derived results, some examples and simulations are provided.