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Discrete‐time H ∞ output feedback for Markov jump systems with uncertain transition probabilities
Author(s) -
Fioravanti André R.,
Gonçalves Alim P.C.,
Geromel José C.
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.2807
Subject(s) - polytope , control theory (sociology) , markov chain , dropout (neural networks) , discrete time and continuous time , convex combination , mathematics , mathematical optimization , regular polygon , computer science , controller (irrigation) , convex optimization , control (management) , discrete mathematics , statistics , geometry , artificial intelligence , machine learning , agronomy , biology
SUMMARY This article addresses theH ∞output feedback control for discrete‐time Markov jump linear systems. With fully known transition probability, sufficient conditions for an internal model based controller design are obtained. For the case where the transition probabilities are uncertain and belong to a convex polytope with known vertices, we provide a sufficient LMI condition that guarantees theH ∞norm of the closed‐loop system is below a prescribed level. That condition can be improved through an iterative procedure. Additionally, we are able to deal with the case of cluster availability of the Markov mode, provided that some system matrices do not vary within a given cluster, an assumption that is suitable to deal with packet dropout models for networked control systems. A numerical example shows the applicability of the design and compares it with previous results. Copyright © 2012 John Wiley & Sons, Ltd.