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Exponential H ∞ filtering for stochastic Markovian jump systems with time delays
Author(s) -
Chen Yun,
Zheng Wei Xing
Publication year - 2012
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.2909
Subject(s) - mathematics , lemma (botany) , exponential stability , bounding overwatch , bounded function , exponential function , filter (signal processing) , basis (linear algebra) , markov process , computer science , mathematical analysis , statistics , ecology , physics , geometry , poaceae , quantum mechanics , nonlinear system , artificial intelligence , computer vision , biology
SUMMARY This paper investigates the problem of exponential H ∞ filtering for stochastic systems with time delays and Markovian jumping parameters. On the basis of Lyapunov–Krasovskii functional theory and generalized Finsler lemma, a delay‐dependent bounded real lemma is established without using any model transformations, bounding techniques for cross terms, or additional free matrix variables. The obtained bounded real lemma guarantees that the filtering error system is both mean‐square exponentially stable and almost surely exponentially stable with a prescribed H ∞ noise attenuation level. Then an exponential H ∞ filter is designed for stochastic retarded Markovian jump systems in terms of a set of LMIs. Meanwhile, the mathematical equivalence of the proposed method to one recent method is presented, but our proposed method is more computationally efficient with fewer matrix variables than that recent method. The validity of the method is verified by a numerical example.Copyright © 2012 John Wiley & Sons, Ltd.