Input/Output-to-State Stability of Impulsive Switched Systems with Time Delays

Abstract

In this paper, we study the input/output-to-state stability (IOSS) of impulsive switched systems with time delays, where the derivative of Lyapunov functions are assumed to be time-varying and mode-dependent. Based on the Lyapunov-Razumikhin method and the mode-dependent average dwell time (MDADT) condition, some Rzaumikhin-type criteria for IOSS of impulsive switched systems with the coexistence of the destabilizing and stabilizing impulses are established. The derivative of Lyapunov functions of subsystems are allowed to be indefinite, which implies that the criteria can be applied to impulsive switched systems involving the coexistence of IOSS and non-IOSS subsystems. Furthermore, under mode-dependent conditions, the dwell time of each subsystem allows to be small or large enough. Finally, two illustrative examples are provided to demonstrate the effectiveness of the proposed results.