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Robust H ∞ filtering for switched linear discrete‐time systems with polytopic uncertainties
Author(s) -
Zhang Lixian,
Shi Peng,
Wang Changhong,
Gao Huijun
Publication year - 2006
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.901
Subject(s) - control theory (sociology) , filter (signal processing) , mathematics , linear system , convex optimization , lyapunov function , linear matrix inequality , filtering problem , stability (learning theory) , discrete time and continuous time , exponential stability , noise (video) , set (abstract data type) , matrix (chemical analysis) , regular polygon , filter design , computer science , mathematical optimization , nonlinear system , materials science , artificial intelligence , image (mathematics) , mathematical analysis , composite material , geometry , control (management) , quantum mechanics , machine learning , statistics , computer vision , programming language , physics
In this paper, the problem of robust H ∞ filtering for switched linear discrete‐time systems with polytopic uncertainties is investigated. Based on the mode‐switching idea and parameter‐dependent stability result, a robust switched linear filter is designed such that the corresponding filtering error system achieves robust asymptotic stability and guarantees a prescribed H ∞ performance index for all admissible uncertainties. The existence condition of such filter is derived and formulated in terms of a set of linear matrix inequalities (LMIs) by the introduction of slack variables to eliminate the cross coupling of system matrices and Lyapunov matrices among different subsystems. The desired filter can be constructed by solving the corresponding convex optimization problem, which also provides an optimal H ∞ noise‐attenuation level bound for the resultant filtering error system. A numerical example is given to show the effectiveness and the potential of the proposed techniques. Copyright © 2006 John Wiley & Sons, Ltd.