Filter design for discrete time‐varying delay systems: three‐term approximation approach

Abstract

In this study, the analysis and design problems of H∞ filtering for a class of discrete-time-varying delay systems are investigated. The authors' attention is focused on the filter design using scaled small gain (SSG) approach guaranteeing the robust asymptotic stability of the filtering error system with a prescribed H∞ performance. A novel transformation model of the filtering error system is obtained via three-term approximation method and input-output approach based on SSG theorem. Then, the desired filter design is obtained through a convex optimisation problem resolution under a set of linear matrix inequality constraints. Finally, the use of many examples from the literature demonstrates the effectiveness of the proposed approach.