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ℋ︁ ∞ and l 2 – l ∞ filtering for two‐dimensional linear parameter‐varying systems
Author(s) -
Wu Ligang,
Wang Zidong,
Gao Huijun,
Wang Changhong
Publication year - 2007
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1169
Subject(s) - parameterized complexity , filter (signal processing) , convex optimization , mathematics , attenuation , noise (video) , linear system , linear matrix inequality , regular polygon , filter design , parameter space , control theory (sociology) , computer science , mathematical optimization , algorithm , mathematical analysis , statistics , physics , geometry , control (management) , artificial intelligence , optics , image (mathematics) , computer vision
In this paper, the ℋ ∞ and l 2 – l ∞ filtering problem is investigated for two‐dimensional (2‐D) discrete‐time linear parameter‐varying (LPV) systems. Based on the well‐known Fornasini–Marchesini local state‐space (FMLSS) model, the mathematical model of 2‐D systems under consideration is established by incorporating the parameter‐varying phenomenon. The purpose of the problem addressed is to design full‐order ℋ ∞ and l 2 – l ∞ filters such that the filtering error dynamics is asymptotic stable and the prescribed noise attenuation levels in ℋ ∞ and l 2 – l ∞ senses can be achieved, respectively. Sufficient conditions are derived for existence of such filters in terms of parameterized linear matrix inequalities (PLMIs), and the corresponding filter synthesis problem is then transformed into a convex optimization problem that can be efficiently solved by using standard software packages. A simulation example is exploited to demonstrate the usefulness and effectiveness of the proposed design method. Copyright © 2007 John Wiley & Sons, Ltd.