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ℋ ∞ and ℋ 2 control design for polytopic continuous‐time Markov jump linear systems with uncertain transition rates
Author(s) -
Morais Cecília F.,
Braga Márcio F.,
Oliveira Ricardo C. L. F.,
Peres Pedro L. D.
Publication year - 2015
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.3329
Subject(s) - mathematics , polytope , control theory (sociology) , lyapunov function , scalar (mathematics) , linear matrix inequality , simplex , transition rate matrix , state (computer science) , mathematical optimization , control (management) , computer science , nonlinear system , algorithm , discrete mathematics , statistics , physics , geometry , quantum mechanics , artificial intelligence
Summary This paper investigates the problems ofℋ ∞ andℋ 2 state feedback control design for continuous‐time Markov jump linear systems. The matrices of each operation mode are supposed to be uncertain, belonging to a polytope, and the transition rate matrix is considered partly known. By appropriately modeling all the uncertain parameters in terms of a multi‐simplex domain, new design conditions are proposed, whose main advantage with respect to the existing ones is to allow the use of polynomially parameter‐dependent Lyapunov matrices to certify the mean square closed‐loop stability. Synthesis conditions are derived in terms of matrix inequalities with a scalar parameter. The conditions, which become LMIs for fixed values of the scalar, can cope withℋ ∞ andℋ 2 state feedback control in both mode‐independent and mode‐dependent cases. Using polynomial Lyapunov matrices of larger degrees and performing a search for the scalar parameter, less conservative results in terms of guaranteed costs can be obtained through LMI relaxations. Numerical examples illustrate the advantages of the proposed conditions when compared with other techniques from the literature. Copyright © 2015 John Wiley & Sons, Ltd.