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

Rui-Hua Wang, Bing-Xin Xue*, and Jing-Bo Zhao
International Journal of Control, Automation, and Systems, vol. 17, no. 8, pp.1921-1934, 2019

Abstract : The problem of H∞ control for discrete-time switched systems is investigated via admissible edgedependent 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.

Keyword : Admissible edge-dependent average dwell time, discrete-time switched systems, H∞ state feedback control, multiple piecewise convex Lyapunov function.

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