Robust filter design for piecewise discrete‐time systems with time‐varying delays

A novel delay‐dependent filtering design approach is developed for a class of linear piecewise discrete‐time systems with convex‐bounded parametric uncertainties and time‐varying delays. The time‐delays appear in the state as well as the output and measurement channels. The filter has a linear full‐order structure and guarantees the desired estimation accuracy over the entire uncertainty polytope. The desired accuracy is assessed in terms of either ??_∞‐performance or ??₂–??_∞ criteria. A new parametrization procedure based on a combined Finsler's Lemma and piecewise Lyapunov–Krasovskii functional is established to yield sufficient conditions for delay‐dependent filter feasibility. The filter gains are determined by solving a convex optimization problem over linear matrix inequalities. In comparison to the existing design methods, the developed methodology yields the least conservative measures since all previous overdesign limitations are almost eliminated. By means of simulation examples, the advantages of the developed technique are readily demonstrated. Copyright © 2009 John Wiley & Sons, Ltd.