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Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities. (English) Zbl 1158.93414
Summary: 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
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