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H2 Dynamic Output Feedback Control for Hidden Markov Jump Linear Systems

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Modeling, Stochastic Control, Optimization, and Applications

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 164))

Abstract

In this note, we discuss the design of H2 dynamic output feedback controllers for a class of jump systems whose switching is induced by a Markov chain. The observation model is based on hidden Markov chains, in which only a random variable conditioned on the jump process of the plant is available to the controller. In this context, we consider a type of sub-optimal ad hoc separation procedure in which a state-feedback controller is given in order to obtain the remaining controller matrices by means of the linear matrix inequality formulation. In the case of perfect observation of the Markov chain, the conditions also become necessary allowing us to calculate optimal H2 controllers also provided by the classical results of the literature. Clusterized and mode-independent controllers can also be synthesized via our formulation. Two illustrative examples are presented.

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Authors and Affiliations

  1. Departamento de Engenharia de Telecomunicações e Controle Escola Politécnica da Universidade de São Paulo, CEP: 05508-010 São Paulo, Brazil

    A. M. de Oliveria & O. L. V. Costa

  2. Université de Lorraine, CNRS, CRAN, F-54000, Nancy, France

    J. Daafouz

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  1. A. M. de Oliveria
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  2. O. L. V. Costa
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  3. J. Daafouz
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Correspondence to A. M. de Oliveria .

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  1. Department of Mathematics, Wayne State University, Detroit, MI, USA

    George Yin

  2. Department of Mathematics, University of Georgia, Athens, GA, USA

    Qing Zhang

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de Oliveria, A.M., Costa, O.L.V., Daafouz, J. (2019). H2 Dynamic Output Feedback Control for Hidden Markov Jump Linear Systems. In: Yin, G., Zhang, Q. (eds) Modeling, Stochastic Control, Optimization, and Applications. The IMA Volumes in Mathematics and its Applications, vol 164. Springer, Cham. https://doi.org/10.1007/978-3-030-25498-8_21

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