Robust \(H_\infty\) control for discrete-time stochastic interval system with time delay (Q460205)

Summary: The robust \(H_\infty\) 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 \(H_\infty\) controller for DTSIS are obtained in terms of linear matrix inequality (LMI) form, and the robust \(H_\infty\) controller is designed. Finally, a numerical example with simulation is given to show the effectiveness and correctness of the designed robust \(H_\infty\) controller.