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This paper investigates Hinfin filtering design problems for discrete time piecewise-linear systems with constant or time-varying delays. Firstly, a novel delay-dependent piecewise Lyapunov-Krasovskii functional (LKF) is proposed, in which both the upper and the lower bound of delays are considered. Then, based on this piecewise LKF, the delay-dependent stability criteria of systems with constant or time-varying delays are obtained, respectively, and piecewise Hinfin filtering design approaches are proposed. It is shown that our stability analysis is less conservative and the corresponding Hinfin filtering can achieve better performance. The filtering parameters can be obtained by solving a set of linear matrix inequalities (LMIs). Simulation examples are also given to illustrate the performance of the proposed approaches.