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filter design for polytopic continuous‐time Markov jump linear systems with uncertain transition rates |
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| Authors: | Cecília F. Morais Márcio F. Braga Márcio J. Lacerda Ricardo C. L. F. Oliveira Pedro L. D. Peres |
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| Affiliation: | School of Electrical and Computer Engineering, University of Campinas – UNICAMP, Campinas, S?o Paulo, Brazil |
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| Abstract: | This paper addresses the problems of  and  full‐order filter design for continuous‐time Markov jump linear systems subject to uncertainties. Different from the available methods in the literature, the main novelty of the proposed approach is the possibility of computing bounds to the  and  norms of the augmented system composed by the uncertain Markov jump linear system plus the robust filter through Lyapunov matrices depending polynomially on the uncertainties affecting independently the matrices of each operation mode and the transition rate matrix. By means of a suitable representation of the uncertainties, the proposed filter design conditions are expressed in terms of linear matrix inequality relaxations associated with searches on scalar parameters. As an additional flexibility, the conditions can be used to synthesize filters with partial, complete, or null Markov mode availability. Numerical experiments illustrate that the proposed approach is more general and can be less conservative than the available methods. Copyright © 2014 John Wiley & Sons, Ltd. |
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| Keywords: | Markov jump linear systems uncertain transition rates polytopic uncertainties HERE and HERE filtering linear matrix inequalities |
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