RobustH_∞filtering for uncertain discrete piecewise time-delay systems

Abstract

This paper investigates the problem of robust H ∞ filter design for uncertain discrete piecewise time-delay systems based on a piecewise Lyapunov functional. The parametric uncertainties are assumed to be time-varying but norm bounded. The purpose is the design of a piecewise filter such that, for all admissible uncertainties, the resulting filtering error system is asymptotically stable and satisfies a prescribed H ∞ performance level. By introducing some different extra matrix variables, a sufficient condition for the solvability of this problem is obtained in terms of linear matrix inequalities (LMIs). When these LMIs are feasible, the explicit expression of a desired piecewise filter is given. Two numerical examples are provided to demonstrate the effectiveness of the proposed design method.