State Feedback Control for Stochastic Nonlinear Systems with Unknown Time Delay

A state feedback stabilization scheme is proposed for a class of strict-feedback stochastic time-delay nonlinear systems. Under assumption that the nonlinear functions of system satisfy linear growth condition, a memoryless linear state feedback controller is designed based on backstepping technique and domination method. By constructing a quartic Lyapunov-Krasoviskii functional, the fourth-moment exponential stabilization of closed-loop system is proved. The simulation example is provided to illustrate the feasibility of the proposed scheme.