Filtering for discrete piecewise linear systems with infinite distributed delays

This paper is concerned with the H
_∞
filtering problem for discrete-time piecewise linear systems subject to external disturbances and time delays. The time delays are assumed to be infinitely distributed in the discrete-time domain. The purpose of the addressed H
_∞
filtering problem is to design a piecewise linear filter such that, for the admissible external disturbances and possible infinite distributed delays, the augmented dynamics is exponentially stable and the H
_∞
performance is guaranteed with a prescribed attenuation level γ. With the aid of the convex optimal method, the filter parameters are obtained in terms of the solution to a set of LMIs which can be solved by the Matlab Toolbox. At last, an illustrative simulation is presented to demonstrate the effectiveness and applicability of the proposed algorithms.