Mean-Square Exponential Stability for Stochastic Control Systems With Discrete-Time State Feedbacks and Their Numerical Schemes in Simulation

Aiming at the qualitative numerical simulation, this article concerns the mean-square exponential stability (MSES) of the stochastic systems with discrete-time state feedbacks and their numerical schemes. A time delay dependent stability criterion is obtained for the underlying system. The Euler-Maruyama and backward Euler-Maruyama schemes are established, and their MSES are proved under the same criterion, which means that the numerical schemes preserve the stability of the continuous model. The illustrative example at the end of this letter shows that the theoretical upper bound for the sampling period limited in the stability criterion is much greater than that obtained by the stability criteria from the literature.