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H ∞ control for discrete‐time Markovian jump linear systems with partly unknown transition probabilities
Author(s) -
Zhang Lixian,
Boukas ElKébir
Publication year - 2008
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.1355
Subject(s) - linearization , discrete time and continuous time , control theory (sociology) , mathematics , jump , markov process , jump process , class (philosophy) , state (computer science) , stochastic matrix , transition (genetics) , matrix (chemical analysis) , control (management) , nonlinear system , computer science , markov chain , algorithm , physics , biochemistry , statistics , chemistry , quantum mechanics , artificial intelligence , gene , materials science , composite material
In this paper, the problem of H ∞ control for a class of discrete‐time Markovian jump linear system with partly unknown transition probabilities is investigated. The class of systems under consideration is more general, which covers the systems with completely known and completely unknown transition probabilities as two special cases. Moreover, in contrast to the uncertain transition probabilities studied recently, the concept of partly unknown transition probabilities proposed in this paper does not require any knowledge of the unknown elements. The H ∞ controllers to be designed include state feedback and dynamic output feedback, since the latter covers the static one. The sufficient conditions for the existence of the desired controllers are derived within the matrix inequalities framework, and a cone complementary linearization algorithm is exploited to solve the latent equation constraints in the output‐feedback control case. Two numerical examples are provided to show the validness and potential of the developed theoretical results. Copyright © 2008 John Wiley & Sons, Ltd.