Input-to-state stability for discrete-time stochastic nonlinear systems

In this paper, the stochastic input-to-state stability(SISS) is discussed for discrete time stochastic nonlinear systems. The definition of SISS for discrete stochastic nonlinear systems is provided. Based on a useful comparison principle, which we provide for discrete time stochastic process, some sufficient conditions on globally asymptotically stable in probability (GASiP) and SISS are provided. As an example, a sufficient condition is provided for discrete time linear stochastic systems. Simulation also illustrate the effectiveness of our results.