Delay-dependent Stability Criterion and H∞ State-feedback Control for Uncertain Discrete-time Switched Systems with Time-varying Delays

The robust stability and H∞ state-feedback control problems for uncertain discrete-time switched systems with time-varying delays are discussed in this paper. The uncertainty is time-varying but norm-bounded. By the switched Lyapunov-Krasovskii functional approach, delay-dependent linear matrix inequality conditions for the delayvarying discrete-time uncertain switched system are developed to guarantee that the switched system is asymptotically stable with an l2 gain smaller than a prescribed scalar under arbitrary switching; Switched state-feedback controller is designed to render the corresponding switched closed-loop system asymptotically stable with an l2 gain measure. Linear matrix inequality approach is employed to the state-feedback controller design. Finally, two numerical examples are given to illustrate the validity of the proposed techniques.