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A less conservative method for designing H ∞ filters for linear time‐delay systems
Author(s) -
Zhang XianMing,
Han QingLong
Publication year - 2009
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.1407
Subject(s) - filter (signal processing) , mathematics , control theory (sociology) , lemma (botany) , interval (graph theory) , lyapunov function , bounded function , set (abstract data type) , stability theory , matrix (chemical analysis) , filtering problem , linear matrix inequality , filter design , computer science , mathematical optimization , nonlinear system , mathematical analysis , combinatorics , control (management) , materials science , artificial intelligence , ecology , composite material , biology , quantum mechanics , computer vision , programming language , physics , poaceae
This paper focuses on H ∞ filtering for linear time‐delay systems. A new Lyapunov–Krasovskii functional (LKF) is constructed by uniformly dividing the delay interval into two subintervals, and choosing different Lyapunov matrices on each subinterval. Based on this new LKF, a less conservative delay‐dependent bounded real lemma (BRL) is established to ensure that the resulting filtering error system is asymptotically stable with a prescribed H ∞ performance. Then, this new BRL is equivalently converted into a set of linear matrix inequalities, which guarantee the existence of a suitable H ∞ filter. Compared with some existing filtering results, some imposed constraints on the Lyapunov matrices are removed through derivation of the sufficient condition for the existence of the filter. Numerical examples show that the results obtained in this paper significantly improve the H ∞ performance of the filtering error system over some existing results in the literature. Copyright © 2008 John Wiley & Sons, Ltd.