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Further results on H ∞ filtering for discrete‐time systems with state delay
Author(s) -
Li Xianwei,
Li Zhicheng,
Gao Huijun
Publication year - 2011
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.1588
Subject(s) - filter (signal processing) , weighting , constant (computer programming) , upper and lower bounds , mathematics , state (computer science) , discrete time and continuous time , control theory (sociology) , matrix (chemical analysis) , filter design , linear matrix inequality , computer science , mathematical optimization , algorithm , control (management) , statistics , mathematical analysis , materials science , artificial intelligence , composite material , computer vision , radiology , programming language , medicine
This article studies the problem of H ∞ filtering for linear discrete‐time systems with state delay. Via delay partitioning idea, two new H ∞ filter design methods are proposed with much less conservatism than most existing results. The improvement lies in constructing two new Lyapunov–Krasovskii functionals by partitioning the known constant lower bound of delay into several segments equally. Using free‐weighting matrix and Jensen inequality methods, two new delay‐dependent bound real lemmas (BRLs) are obtained, which depend on both the delay and the partitioning number. Based on the obtained BRLs, new H ∞ filter design approaches are proposed in terms of linear matrix inequalities. The results are immediately extended to multiple time delay case and polytopic uncertain case, respectively. Three numerical examples are presented to illustrate the effectiveness and advantage of the proposed approaches. Copyright © 2010 John Wiley & Sons, Ltd.