Abstract: This paper discusses stability and stabilization for a class of discrete-time singular Markov jump systems with partly unknown transition probabilities. By introducing slack matrix variables, a sufficient condition is obtained to guarantee stochastic stability of open-loop systems. A method for designing state feedback controller is then proposed. These conditions are given in terms of linear matrix inequalities (LMIs). A numerical example is given to show effectiveness and less conservatism of the obtained results.

Key words: linear matrix inequality (LMI), stability, transition probability, jump system, stabilization