Filtering of discrete-time Markov jump linear systems with uncertain transition probabilities

This article addresses the filtering design problem for discrete‐time Markov jump linear systems (MJLS) under the assumption that the transition probabilities are not completely known. We present the methods to determine ℋ︁2‐ and ℋ︁∞‐norm bounded filters for MJLS whose transition probability matrice...

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Bibliographic Details
Published in:International journal of robust and nonlinear control 2011-04, Vol.21 (6), p.613-624
Main Authors: Gonçalves, Alim P. C., Fioravanti, André R., Geromel, José C.
Format: Article
Language:English
Subjects:
Design engineering
discrete-time Markov jump linear systems
Filtering
Filtration
linear matrix inequalities
Linear systems
Markov processes
Mathematical models
probability transition uncertainty
robust filtering
Transition probabilities
Uncertainty
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Summary:This article addresses the filtering design problem for discrete‐time Markov jump linear systems (MJLS) under the assumption that the transition probabilities are not completely known. We present the methods to determine ℋ︁2‐ and ℋ︁∞‐norm bounded filters for MJLS whose transition probability matrices have uncertainties in a convex polytope and establish an equivalence with the ones with partly unknown elements. The proposed design, based on linear matrix inequalities, allows different assumptions on Markov mode availability to the filter and on system parameter uncertainties to be taken into account. Under mode‐dependent assumption and internal model knowledge, observer‐based filters can be obtained and it is shown theoretically that our method outperforms some available ones in the literature to date. Numerical examples illustrate this claim. Copyright © 2010 John Wiley & Sons, Ltd.
ISSN:1049-8923
1099-1239
1099-1239
DOI:10.1002/rnc.1610