Asymptotic Behaviour of Jump Linear Systems in Continuous Time

  • M. Mariton
  • P. Bertrand
Conference paper
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 83)


This paper considers the optimal control of a class of stochastic continuous-time linear systems with sudden changes in parameters. The jumps of parameters from one value to another are described by a finite-state Markov chain. When the cost-function is quadratic, the optimal Jump Linear Quadratic control involves a set of coupled Riccati equations. The asymptotic behaviour of this set is studied here. Necessary and sufficient conditions are derived for the existence of an optimal steady-state feedback gain in terms of stabilizability and detectability. In that respect, the conditions obtained are formally identiCal to the conditions of the deterministic Linear Quadratic problem. However, stabilizability and detectability must now be defined in a stochastic sense. As will be seen in the various examples that illustrate the paper, this leads to some specific and unexpected properties of Jump Linear Quadratic systems.


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Copyright information

© Springer Science+Business Media Dordrecht 1986

Authors and Affiliations

  • M. Mariton
    • 1
  • P. Bertrand
    • 1
  1. 1.Laboratoire des Signaux et SystèmesCNRS-ESEGif-sur-YvetteFrance

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