Stabilization of a class of stochastic nonlinear time-delay systems

Abstract

In this paper, the stabilization problem is considered for a class of nonlinear continuous stochastic systems with state delays. The purpose of this problem is to design a state feedback controller such that the closed- loop system is exponentially stable (or exponentially ultimately bounded) in the mean square, for all admissible nonlinearities and time-delays. We first investigate the sufficient conditions for the nonlinear stochastic time-delay systems to be stable, and then derive the explicit expression of the desired controller gains. A numerical simulation example is provided to show the usefulness of the proposed design method.