Robust <i>l</i> ₂ – <i>l</i> _∞ filtering for switched linear discrete time-delay systems with polytopic uncertainties

Abstract

The problem of robust l2–l∞ filtering for switched linear discrete-time systems with polytopic uncertainties and time-varying delays is investigated. The time delay is assumed to be time-varying and bounded, which covers constant delay and mode-dependent constant delays as special cases. A robust switched linear filter is designed based on the mode-switching idea and a parameter-dependent stability approach such that the corresponding filtering error system is robustly asymptotically stable and achieves a prescribed l2–l∞ performance index for all admissible uncertainties. The existence conditions for such a filter, dependent on the upper and lower bounds of time-varying delays, are formulated in terms of a set of linear matrix inequalities. By solving that corresponding convex optimisation problem, the desired filter is obtained and an optimal l2–l∞ noise-attenuation level bound of the resulting filtering error system is guaranteed as well. A numerical example is given to show the feasibility and potential of the theoretical results.