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.


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
Full Text: DOI


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