Delay-Range-Dependent H∞ Control for Stochastic Systems with Time Delay

This paper deals with the problem of robust H-infinity control for a class of uncertain stochastic systems with time-varying delay. By applying an appropriate Lpapunov-Krasovskii functional and combining an improved linearization approach of the nonlinear matrix inequality with the free-weighting matrix method, some new delay-dependent and delay-range-dependent stabilization criteria for the stochastic systems are derived in terms of linear matrix inequalities (LMIS). When these LMIS are feasible, an explicit expression of a desired H-infinity controller is given. Designed state feedback controller, based on the obtained criteria, ensure asymptotically stable in the mean square sense and a prescribed H-infinity performance level of the resulting closed-loop system for all admissible uncertainties.