Time-varying H∞ Control for Discrete-time Switched Systems with Admissible Edge-dependent Average Dwell Time

The problem of H∞ control for discrete-time switched systems is investigated via admissible edge-dependent average dwell time (AED-ADT) method in this paper. By virtue of a convex combination of positive definite matrices, a novel multiple piecewise convex Lyapunov function (MPCLF) is designed, which can relax the restricted conditions of Lyapunov functions at switching points and interval interior points. Based on the MPCLF approach, the time-varying H∞ state feedback controllers, guaranteeing that the corresponding closed-loop system is globally uniformly exponentially stable (GUES) with a prescribed H∞ performance, are established for the considered switched system. Finally, three numerical examples are provided to illustrate the effectiveness of the proposed approaches.