Output feedback varvec{mathcal {H}}_{{varvec{infty }}} control of stochastic nonlinear time-delay systems with state and disturbance-dependent noises

This paper is concerned with the output feedback (mathcal {H}_infty ) 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 (hat{o}) -type differential equation with state and disturbance contaminated by white noises. The design of the output feedback (mathcal {H}_infty ) 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 (mathcal {H}_infty ) controller. It is shown that the output feedback (mathcal {H}_infty ) 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.