Output feedback ℋ ∞ control of stochastic nonlinear time-delay systems with state and disturbance-dependent noises

This paper is concerned with the output feedback ℋ ∞ control problem for a class of stochastic nonlinear systems with time-varying state delays; the system dynamics is governed by the stochastic time-delay It ̂ -type differential equation with state and disturbance contaminated by white noises. The design of the output feedback ℋ ∞ control is based on the stochastic dissipative theory. By establishing the stochastic dissipation of the closed-loop system, the delay-dependent and delay-independent approaches are proposed for designing the output feedback ℋ ∞ controller. It is shown that the output feedback ℋ ∞ control problem for the stochastic nonlinear time-delay systems can be solved by two delay-involved Hamilton-Jacobi inequalities. A numerical example is provided to illustrate the effectiveness of the proposed methods.