Exponential stability theorems for discrete-time impulsive stochastic systems with delayed impulses

This paper investigates the pth moment exponential stability and almost sure exponential stability of discrete-time impulsive stochastic systems with delayed impulses. By using Razumikhin technique, several sufficient conditions for the exponential stability of discrete-time impulsive stochastic systems are derived, which extends the corresponding results for discrete-time stochastic systems without impulses. Both the stability results that impulses act as perturbation and the stability results that impulses act as stabilizer are obtained. Three examples and simulations are also presented to illustrate the effectiveness of the obtained results. (C) 2019 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.