<i>p</i>th moment exponential input‐to‐state stability of nonlinear discrete‐time impulsive stochastic delay systems

Abstract

Summary This paper investigates the p th moment exponential input‐to‐state stability (ISS) of nonlinear discrete‐time impulsive stochastic delay systems. By employing Lyapunov functionals, some p th moment exponential ISS criteria are provided. The obtained results show that a discrete‐time stochastic delay system can become p th moment exponential input‐to‐state stable by impulsive controls even if it may be not input‐to‐state stable itself. On the other hand, the original system without impulses can retain its ISS property with appropriate destabilizing impulses. As an application, the theoretical results are used to test the ISS for a class of recurrent neural networks under stochastic perturbations. Finally, a numerical example is presented to illustrate the effectiveness of the results.