H∞ Control for Markovian Jump Systems with Partly Known Transition Probabilities in Discrete-time Domain

In this paper, the H∞ controller design problem is investigated for the discrete-time Markovian jump linear system in the presence of incomplete transition descriptions. A less conservative criterion is presented such that the considered system is stochastically stable with a guaranteed H∞ performance index by using the properties of the transition probabilities. In addition, a H∞ state-feedback controller is proposed for the discrete-time Markovian jump system with incomplete transition description via LMI formulation. Finally, some simulation results are given to verify the effectiveness of the presented methods.