Robust exponential l 2 − l ∞ control for discrete‐time switched system: A cone complement linearization method

SUMMARY The robust exponential l 2  −  l  ∞  control problem is considered in this paper for discrete‐time switched systems with both time‐varying delay and norm‐bounded parameter uncertainties. An exponential l 2  −  l  ∞  performance index is first introduced for the discrete‐time switched systems. The designed controller is a memory exponential l 2  −  l  ∞  controller. By introducing an average dwell time approach and a Lyapunov–Krasovskii functional technique, some sufficient criteria guaranteeing exponential stability are presented, and the desired memory exponential l 2  −  l  ∞  controller is established by resorting to a cone complement linearization method. Some results on exponential stability using memoryless exponential l 2  −  l  ∞  controller and asymptotical stability with traditional l 2  −  l  ∞  performance index are also established. Finally, a numerical example is provided to demonstrate that the proposed approach can lead to less conservatism compared with the developed result using memoryless exponential l 2  −  l  ∞  controller and asymptotical stability analysis with traditional l 2  −  l  ∞  performance index. Copyright © 2011 John Wiley & Sons, Ltd.