Exponential l2 − l∞ filtering for discrete-time switched systems under a new framework

SUMMARY In this paper, a robust exponential l2 − l∞ filtering problem is addressed for discrete‐time switched systems with polytopic uncertainties. The purpose of robust exponential l2 − l∞ filtering is to design a filter such that the resulting filtering error system is robustly exponentially stable with a decay rate and a prescribed exponential l2 − l∞ performance index. The robust exponential l2 − l∞ filtering problem is solved via an average dwell time approach. Sufficient conditions in terms of strict LMI are derived for checking the robust exponential stability of a filter. An explicit expression for the desired robust exponential filter is also given. Finally, a numerical example is provided to demonstrate the potential and effectiveness of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.