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Stabilization of Markovian jump linear system over networks with random communication delay. (English) Zbl 1158.93412
Summary: This paper is concerned with the stabilization problem for a networked control system with Markovian characterization. We consider the case that the random communication delays exist both in the system state and in the mode signal which are modeled as a Markov chain. The resulting closed-loop system is modeled as a Markovian jump linear system with two jumping parameters, and a necessary and sufficient condition on the existence of stabilizing controllers is established. An iterative linear matrix inequality approach is employed to calculate a mode-dependent solution. Finally, a numerical example is given to illustrate the effectiveness of the proposed design method.

MSC:
93E15 Stochastic stability in control theory
93C05 Linear systems in control theory
60J75 Jump processes (MSC2010)
60J05 Discrete-time Markov processes on general state spaces
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