Abstract
AbstractThis paper is concerned with the reliable H∞ filtering problem against sensor failures for a class of discrete‐time systems with simultaneous sector‐bounded nonlinearities and time‐varying delay. The purpose of the paper is to design a filter such that the filtering error systems are asymptotically stable and meet the prescribed H∞ norm constraint in normal case as well as in sensor failure case. Sufficient delay‐dependent conditions for the existence of such a filter are obtained by using appropriate Lyapunov–Krasovskii functional and linear matrix inequality techniques. Moreover, we adopt the slack variable method to realize the decoupling between the Lyapunov matrix and the system dynamic matrices, which makes us enable to adopt different Lyapunov matrices for the normal and the sensor failure cases, respectively. Numerical examples are also provided to demonstrate the effectiveness of the proposed methods. Copyright © 2009 John Wiley & Sons, Ltd.
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