Considering the linear time-varying uncertain singular system, by using the analysis method of matrix inequality, the concepts of robust stability and quadratic stability for the linear time-varying uncertain singular system are proposed. Matrix inequalities for this kind of systems are established. The problems of robust control for this kind of systems are transformed to solve the matrix inequality problem, so that the necessary and sufficient conditions of robust stability and quadratic stability are obtained for the system, and the design methods for state feedback robust stabilization controllers are presented. Finally, a numerical example is provided to illustrate the feasibility of the proposed method.