Robust Stability and H∞ Stabilization of Switched Systems with Time-Varying Delays Using Delta Operator Approach

This paper considers the problems of the robust stability and robust H-infinity controller design for time-varying delay switched systems using delta operator approach. Based on the average dwell time approach and delta operator theory, a sufficient condition of the robust exponential stability is presented by choosing an appropriate Lyapunov-Krasovskii functional candidate. Then, a state feedback controller is designed such that the resulting closed-loop system is exponentially stable with a guaranteed H-infinity performance. The obtained results are formulated in the form of linear matrix inequalities (LMIs). Finally, a numerical example is provided to explicitly illustrate the feasibility and effectiveness of the proposed method.