Filtering for Discrete-Time Delay Systems

Theproblemof robust l 2 -l ∞ filtering for discrete-time systemwith interval time-varying delay and uncertainty is investigated, where the time delay and uncertainty considered are varying in a given interval and norm-bounded, respectively. The filtering problem based on the l 2 -l ∞ performance is to design a filter such that the filtering error system is asymptotically stable with minimizing the peak value of the estimation error for all possible bounded energy disturbances. Firstly, sufficient l 2 -l ∞ performance analysis condition is established in terms of linearmatrix inequalities (LMIs) for discrete-time delay systems by utilizing reciprocally convex approach. Then a less conservative result is obtained by introducing some variables to decouple the Lyapunov matrices and the filtering error system matrices. Moreover, the robust l 2 -l ∞ filter is designed for systems with time-varying delay and uncertainty. Finally, a numerical example is given to demonstrate the effectiveness of the filter design method.