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This note focuses on a class of stochastic time-delay nonlinear systems. The problem we address is to design a controller such that the closed-loop system is exponentially stable. It is shown that the stabilization via output feedback can be solved by a Lyapunov-based recursive design method. Index Terms--Backstepping, output feedback, stabilization, stochastic time-delay nonlinear system.

In this note, we study the problem of output-feedback control design for a class of strict feedback stochastic nonlinear systems. Under an infinite-horizon risk-sensitive cost criterion, the controller designed can guarantee an arbitrary small long-term average cost for arbitrary risk-sensitivity parameter and achieve boundedness in probability for the closed-loop system, using the integrator backstepping methodology. Furthermore, the controller preserves the equilibrium at the origin of the nonlinear system. Index Terms--Bounded in probability, integrator backstepping, risk-sensitive control, strict-feedback stochastic nonlinear systems.

This note focuses on a class of stochastic time-delay nonlinear systems. The problem we address is to design a controller such that the closed-loop system is exponentially stable. It is shown that the stabilization ia state feedback can be solved by a Lyapunov-based recursive design method. Index Terms--Backstepping, stabilization, state feedback, stochastic time-delay nonlinear system.