This paper is concerned with the problem of robust stabilization for generalized state-space systems with parameter uncertainty. The parameter uncertainty under consideration is time-invariant and unknown, but is norm-bounded. The problem we address is to design a state feedback controller such that the resulting closed-loop system is regular, impulse-free and stable for all admissible uncertainties. Via the notion of 'stabilizability and impulse eliminatibility' the robust stabilization problem is solved. Necessary and sufficient conditions for stabilizability and impulse eliminatibility are derived. When these conditions are satisfied, the desired stabilization state feedback controller can be constructed through finding parameters satisfying a certain matrix equation. Finally, an illustrative example is given to show the feasibility of the proposed technique.