Robust H∞ control for stochastic systems with nonlinearity, uncertainty and time-varying delay

This paper deals with the problems of robust stochastic stabilization and $H_{\infty }$ control for uncertain stochastic systems with time‐varying delay and nonlinear perturbation. System uncertainties are assumed to be norm bounded and time delay is assumed to be bound and time varying with delay‐derivative bounded by a constant, which may be greater than one. First, new delay‐dependent criterion is proposed by exploiting delay‐partitioned Lyapunov–krasovskii functional and by employing tighter integral equalities to estimate the upper bound of the stochastic differential of Lyapunov–krasovskii functional without ignoring some useful terms. Second, based on the criterion obtained, a delay‐dependent criterion for the existence of a state feedback $H_{\infty }$ controller that ensures robust stochastic stability and a prescribed $H_{\infty }$ performance level of the closed‐loop system for all admissible uncertainties is proposed. These developed results have advantages over some previous ones, in that they involve fewer matrix variables but have less conservatism and they also enlarge the application scope. New sufficient conditions are presented in terms of linear matrix inequality. Numerical examples are used to illustrate the effectiveness and feasibility of the proposed method.