Feedback controller design of discrete-time singular markovian jump systems with partial transition probabilities

Stabilization control problem is investigated for a class of discrete-time singular Markovian jump systems with partial transition probabilities. A sufficient condition for the open-loop system to be regular, causal and stochastically stable is proposed in the form of a set of strict linear matrix inequalities. The proposed sufficient condition uses the information of unknown parts of transition probabilities by equivalent transformation instead of minimizing method, so it is less conservative. Furthermore, for the considered systems, a mode-dependent state feedback controller is designed to make sure that the closed-loop system is regular, causal and stochastically stable. Finally, a numerical example is given to demonstrate the effectiveness of the proposed results.