For a class of discrete-time Markov jump singular systems, the stability and stabilization problems are
investigated. The systems under consideration are more general, since transition probabilities of the mode jumps can be partly unknown, which includes the systems with completely known and completely unknown transition probabilities as two special cases. Some sufficient conditions for the Markov jump singular systems to be regular, causal and stochastically stable are derived based on strict linear matrix inequality(LMI) approach, and the designs of the state feedback and output feedback controllers are presented. Finally, a numerical example demonstrates the effectiveness of the proposed method.