Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities.

*(English)*Zbl 1158.93414Summary: The stability and stabilization problems of a class of continuous-time and discrete-time Markovian Jump Linear System (MJLS) with partly unknown transition probabilities are investigated. The system under consideration is more general, which covers the systems with completely known and completely unknown transition probabilities as two special cases – the latter is hereby the switched linear systems under arbitrary switching. Moreover, in contrast with the uncertain transition probabilities studied recently, the concept of partly unknown transition probabilities proposed in this paper does not require any knowledge of the unknown elements. The sufficient conditions for stochastic stability and stabilization of the underlying systems are derived via LMIs formulation, and the relation between the stability criteria currently obtained for the usual MJLS and switched linear systems under arbitrary switching, are exposed by the proposed class of hybrid systems. Two numerical examples are given to show the validity and potential of the developed results.

##### MSC:

93E15 | Stochastic stability in control theory |

60J05 | Discrete-time Markov processes on general state spaces |

60J25 | Continuous-time Markov processes on general state spaces |

93C05 | Linear systems in control theory |

##### Keywords:

Markovian jump linear systems; switched linear systems; stability and stabilization; partly unknown transition probabilities; linear matrix inequality (LMI)
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\textit{L. Zhang} and \textit{E.-K. Boukas}, Automatica 45, No. 2, 463--468 (2009; Zbl 1158.93414)

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##### References:

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