This paper deals with the class of continuous-time singular linear systems with random abrupt changes. The state feedback stabilization and its robustness for this class of systems with norm bounded uncertainties are tackled. Sufficient conditions for designing either a stabilizing or a robust stabilizing controller are developed in the LMI setting. The developed sufficient conditions are used to synthesis the state feed- back controller that guarantees either the nominal system or the uncertain system is piecewise regular, impulse free and stochastically stable or robust stochastically stable.