Stabilization of Markovian jump linear system over networks with random communication delay.

*(English)*Zbl 1158.93412Summary: 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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##### References:

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