The robust stability and stabilization,and H-infinity control problems for discrete-time Markovian jump singular systems with parameter uncertainties are discussed.Based on the restricted system equivalent(r.s.e.)transformation and by introducing new state vectors,the singular system is transformed into a discrete-time Markovian jump standard linear system,and the linear matrix inequality(LMI)conditions for the discrete-time Markovian jump singular systems to be regular,causal,stochastically stable,and stochastically stable with γ-disturbance attenuation are obtained,respectively.With these conditions,the robust state feedback stochastic stabilization problem and H-infinity control problem are solved,and the LMI conditions are obtained.A numerical example illustrates the effectiveness of the method given in the paper.