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Exponential H ∞ filter design for stochastic time‐varying delay systems with Markovian jumping parameters
Author(s) -
Ma Li,
Da Feipeng
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.1477
Subject(s) - control theory (sociology) , filter (signal processing) , mathematics , jumping , exponential growth , exponential stability , exponential function , markov process , expression (computer science) , matrix (chemical analysis) , filter design , class (philosophy) , computer science , mathematical analysis , statistics , control (management) , nonlinear system , physics , physiology , materials science , quantum mechanics , artificial intelligence , composite material , computer vision , biology , programming language
In this paper, the exponential H ∞ filter design problem is investigated for a general class of stochastic time‐varying delay system with Markovian jumping parameters. The stochastic uncertainties appear in both the dynamic and the measurement equations and the state delay is assumed to be time‐varying. Attention is focused on the design of mean‐square exponentially stable and Markovian jump filter such that the filtering error systems are mean‐square exponentially stable and the estimation error satisfies a given H ∞ performance. By introducing some slack matrix variables, delay‐dependent sufficient conditions for the solvability of the above problem are presented in terms of linear matrix inequalities (LMIs). In addition, the decay rate can be a given positive value without any other constraints. When the proposed LMIs are feasible, an explicit expression of the desired H ∞ filter can be given. A numerical example is provided to illustrate the effectiveness of the proposed design approach. Copyright © 2009 John Wiley & Sons, Ltd.