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Numerical Solution for Linear-Quadratic Control Problems of Markov Jump Linear Systems and Weak Detectability Concept

Author

Listed:
  • J.B.R. Do Val

    (University of Campinas)

  • E.F. Costa

    (University of Campinas)

Abstract

A method for solving the linear-quadratic problem of Markov jump linear systems is developed in this paper, relying on the assumption of weak detectability. The concept of weak detectability generalizes previous concepts relevant to this class of systems, and most importantly, it allows us to revisit the quadratic control problem. In the main result of the paper, we show that, for weakly detectable systems, the solution obtained with the new method converges to the solution of the coupled algebraic Riccati equation that arises in the control problem if and only if the system is mean-square stabilizable. The paper shows how the concepts and the method involved are applied by means of numerical examples and comparisons.

Suggested Citation

  • J.B.R. Do Val & E.F. Costa, 2002. "Numerical Solution for Linear-Quadratic Control Problems of Markov Jump Linear Systems and Weak Detectability Concept," Journal of Optimization Theory and Applications, Springer, vol. 114(1), pages 69-96, July.
    • Handle: RePEc:spr:joptap:v:114:y:2002:i:1:d:10.1023_a:1015412121001
    DOI: 10.1023/A:1015412121001
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    References listed on IDEAS

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    1. J. B. R. Do Val & J. C. Geromel & O. L. V. Costa, 1999. "Solutions for the Linear-Quadratic Control Problem of Markov Jump Linear Systems," Journal of Optimization Theory and Applications, Springer, vol. 103(2), pages 283-311, November.
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