Sliding mode control of discrete-time switched systems with time-delay

In this paper, the problem of sliding mode control of a discrete-time switched system with time-varying delay is investigated. By using the average dwell time approach and the piecewise Lyapunov function technique, a sufficient condition is proposed to guarantee the exponential stability of the switched systems with time delays. The conservation of the obtained results is reduced by employing the delay partitioning method and the free-weighting matrix technique. A sliding mode controller has been designed to force the closed-loop system to be driven onto a prescribed sliding surface and maintained there for all subsequent time. Finally, a numerical example is given to illustrate the effectiveness of the proposed theory.