Abstract: This paper is concerned with the problems of robust H∞ control for uncertain singular systems. The system under consideration is subjected to time-varying norm-bounded uncertainties in both state and input matrices. The problem we address is the design of state feedback controllers such that the closed-loop system is regular, impulse-free, as well as satisfying a prescribed H∞ norm bound constraint for all admissible uncertainties. In the light of the notion of 'generalized quadratic stabilizability with H. performance index', the robust H∞ control problem is solved; furthermore, the desired robust H∞ state feedback control law can be constructed in terms of solutions to a certain linear matrix inequality.