Improved Delay-Dependent $H_{\infty }$ Filtering Design for Discrete-Time Polytopic Linear Delay Systems

Abstract

This brief revisits the problem of delay-dependent robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> filtering design for discrete-time polytopic linear systems with interval-like time-varying delay. Under the condition whether the unknown parameters can be measured online or not, a parameter-dependent or a parameter-independent filter is respectively developed which guarantees the asymptotic stability of the resulting filtering error system with robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> performance gamma. It is shown that by using a new linearization technique incorporating a bounding technique, a unified framework can be developed such that the full-order and reduced-order, the parameter-dependent and parameter-independent filters can be obtained by solving a set of linear matrix inequalities. Finally, a numerical example is provided to illustrate the effectiveness and merits of the proposed approach.