Delay-dependent robust H∞ control for uncertain stochastic systems with time-varying delays in state and control input

This article deals with the robust H∞ control problem for uncertain stochastic systems with time-varying delays in state and control input. The time delay is assumed to be a time-varying continuous function varying in an interval and uncertainties are assumed to be norm bounded. New delay-dependent criteria for the existence of memoryless state feedback H∞ controller are proposed to guarantee robust asymptotic stability in the mean square as well as the prescribed H∞ performance level of the closed-loop systems for all admissible uncertainties. The main contribution of this article is the instrumental idea of delay decomposing, which leads the resultant conditions to be much less conservative than the existing results in the literature with the decomposing getting thinner. By using free-weighting matrices and a new technique to estimate the upper bound of the stochastic differential of Lyapunov–Krasovskii functional candidate, new delay-dependent conditions are derived by considering the relationship among the time-varying delay and its lower and upper bounds without ignoring any useful terms. The advantage of the results proposed in this article lies in their reduced conservatism, as shown via illustrative examples, which also demonstrates the effectiveness of the proposed method.