Stability of impulsive and switched stochastic delay systems via the event-triggered impulsive mechanism

Abstract

Under the event-triggered impulsive mechanism, this work introduces the pth moment (integral) input-to-state stability (p-(i)ISS) for a general group of impulsive and switched stochastic delay systems. Using the means of mode-dependent average dwell time and mode-dependent average impulsive interval, some sufficient conditions of p-ISS and p-iISS are supplied. By incorporating the input of subsystems and impulses into the triggering functions, two distinct types of event-triggered impulsive constraint is proposed, which is defined as mode-dependent event-triggered impulsive mechanism with input (MDETIMI). Different from the traditional event-triggered impulsive control, two MDETIMI strategy are individually discussed, which one is the supremum of K∞ function of subsystem input and the superposition of impulsive input, and the other is the integral of K∞ function of subsystem input and the superposition of impulsive input. Moreover, it is unveiled that even with the indeterminate derivatives of the Lyapunov functions, the Zeno phenomenon can effectively be avoided by using MDETIMI strategy. Finally, an example shows the effectiveness and practicability of the results.