Stabilization of discrete-time singular Markov jump systems

The problems of stability and stabilization are investigated for a kind of discrete-time singular Markov jump systems with partly unknown transition probabilities. Including two special cases of completely known and completely unknown transition probabilities, the proposed systems with partly unknown transition probabilities are more practical. A sufficient condition for stochastic stability of open-loop discrete-time singular Markov jump systems is derived from the results of discrete-time Markov jump systems by employing linear matrix inequality technique. Moreover, a criterion for feedback stabilization of closed-loop systems is proposed in terms of a set of linear matrix inequalities. Finally, a numerical example is given to illustrate the validity of the proposed results.