Stability Analysis for a class of Stochastic Nonlinear Systems Based on The Approximate Discrete-Time Models

In this paper, exponential mean-square stability for a class of stochastic nonlinear systems based on their approximate models is introduced. Firstly, the Euler-Maruyama(EM) approximate discrete-time model of this class of systems is given. Secondly, based on approximate discrete-time model of the given systems, we provide a simpler and more convenient controller design method to stabilize the closed-loop system. And then, the multi-step consistency between the exact discrete-time model and the EM approximate discrete-time model is established. Finally, the stability relationship between the original system and its EM approximate model based on their multi-step consistency is studied. Moreover, a numerical example is provided to demonstrate the effectiveness of the proposed approach.