Input-to-state stability of impulsive stochastic delayed systems under linear assumptions

Abstract

In this paper, the input-to-state stability (ISS), integral-ISS (iISS) and stochastic-ISS (SISS) are investigated for impulsive stochastic delayed systems. By means of the Lyapunov–Krasovskii function and the average impulsive interval approach, the conditions for ISS-type properties are derived under linear assumptions, respectively, for destabilizing and stabilizing impulses. It is shown that if the continuous stochastic delayed system is ISS and the impulsive effects are destabilizing, then the hybrid system is ISS with respect to a lower bound of the average impulsive interval. Moreover, it is unveiled that if the continuous stochastic delayed system is not ISS, the impulsive effects can successfully stabilize the system for a given upper bound of the average impulsive interval. An improved comparison principle is developed for impulsive stochastic delayed systems, which facilitates the derivations of our results for ISS/iISS/SISS. An example of networked control systems is provided to illustrate the effectiveness of the proposed results.