Stabilization Analysis and Synthesis of Discrete-Time Descriptor Markov Jump Systems with Partially Unknown Transition Probabilities

A sufficient condition for the open loop system to be regular, causal and stochastically stable is proposed for a class of discrete-time descriptor Markov jump systems with partly unknown transition probabilities. The proposed criteria are in the form of a set of strict linear matrix inequalities and convenient for numerical realization. The presented condition used the information of unknown transition probabilities in an effective way and is less conservative. Furthermore, the stabilization control of the researching systems is realized by designing the state feedback controller to make the close-looped systems be regular, causal and stochastically stable. At last, a numerical example is given to demonstrate the validity of the proposed results.