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Mean square stabilization of discrete-time switching Markov jump linear systems. (English) Zbl 1411.93185

Summary: This paper considers a special class of hybrid system called switching Markov jump linear system. The system transition is governed by two rules. One is Markov chain and the other is a deterministic rule. Furthermore, the transition probability of the Markov chain is not only piecewise but also orchestrated by a deterministic switching rule. In this paper, the mean square stability of the systems is studied when the deterministic switching is subject to two different dwell time conditions, ie, having a lower bound and having both lower and high bounds. The main contributions of this paper are two relevant stability theorems for the systems under study. A numerical example is provided to demonstrate the theoretical results.

MSC:

93E15 Stochastic stability in control theory
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
60J75 Jump processes (MSC2010)
93C55 Discrete-time control/observation systems
93C05 Linear systems in control theory
93B03 Attainable sets, reachability
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
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References:

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