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

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 (LMI) approach is employed to calculate a mode-dependent solution. Finally, a numerical example is given to illustrate the effectiveness of the proposed design method.