Robust output-feedback stabilization for a class of uncertain stochastic nonlinear systems with time-varying time delays

In this paper, robust output-feedback stabilization is presented for a class of uncertain stochastic nonlinear systems with time-varying time delays. First, the conditions of existence and uniqueness of the solution process are provided and two new stability notions are introduced for stochastic time-delay systems. Based on these preparations, for a class of uncertain stochastic nonlinear systems with time-varying time delays, a systematic design procedure is presented for a memoryless output-feedback control law. It is shown that under the control law based on a reduced-order and memoryless observer, the equilibrium of the closed-loop system is globally asymptotically stable in probability. An example is given to show the effectiveness of the proposed approach.