In this paper, the problem of controller design for Markovian singular systems with discontinuities (MSSD) is investigated. Sufficient conditions to guarantee that the unforced system is regular, impulse-free and stochastically stable in mean square sense with an norm bound constraint, are provided. The derived conditions are expressed in terms of a set of linear matrix inequalities (LMIs), which can be solved by using existing linear algorithms. Also, based on this result, a memoryless State feedback control which ensures the piecewise regularity, the absence of impulsive behavior and the stochastic stability in mean square sense of the closed-loop systems, is proposed by combining the LMI technique, the cone complementarity approach and the sequential linear programming matrix method (SLPMM). A numerical example is given to demonstrate the effectiveness of the proposed methods.