In this paper, the problem of stability and stabilization of Markov jumping singular systems with discontinuities and saturating inputs is addressed. The design procedure via linear matrix inequality technique (LMI) and the sequential linear programming matrix methods (SLPMM), are used to determine simultaneously a state feedback control and an associated domain of safe admissible states for which the regularity, the absence of impulsive behavior and the stochastic stability in mean square sense of the closed-loop systems are guaranteed. A numerical example is provided to demonstrate the effectiveness of the proposed methods.