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Filtering of discrete‐time Markov jump linear systems with uncertain transition probabilities
Author(s) -
Gonçalves Alim P. C.,
Fioravanti André R.,
Geromel José C.
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.1610
Subject(s) - polytope , discrete time and continuous time , observer (physics) , markov chain , bounded function , filter (signal processing) , mathematics , filtering problem , stochastic matrix , transition rate matrix , norm (philosophy) , equivalence (formal languages) , linear system , linear matrix inequality , jump , computer science , mathematical optimization , filter design , discrete mathematics , statistics , quantum mechanics , political science , law , computer vision , mathematical analysis , physics
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 ℋ 2 ‐ and ℋ ∞ ‐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.