Robust H∞ Control for Discrete-Time Stochastic Interval System with Time Delay

The robust H∞ control problem for discrete-time stochastic interval system (DTSIS) with time delay is investigated in this paper. The stochastic interval system is equivalently transformed into a kind of stochastic uncertain time-delay system firstly. By constructing the appropriate Lyapunov-Krasovskii functional, the sufficient conditions for the existence of the robust H∞ controller for DTSIS are obtained in terms of linear matrix inequality (LMI) form, and the robust H∞ controller is designed. Finally, a numerical example with simulation is given to show the effectiveness and correctness of the designed robust H∞ controller.