Abstract: This paper is concerned with the robust control problems for uncertain discrete-time singular systems with disk pole constraints. First of all, we discuss the uncertain discrete-time singular system without control input matrix perturbation. The concept of generalized quadratic D-stabilizability is put forward for uncertain discretetime singular systems. A method of designing the state feedback controller is presented based on some matrix inequalities and the generalized Riccati equation, so that the singular closed-loop system is regular, causal, and satisfies that all finite closed-loop poles are located within a pre-assigned circular region for all admissible parameter uncertainties. Secondly, we discuss the uncertain discrete-time singular system with control input matrix perturbation. The condition for the existence of desired robust state feedback gain matrix is obtained; furthermore, the analytical expression of the desired robust state feedback gain matrix is also derived. Finally. a numerical example is given to illus trate the effectiveness of the proposed approach.