Sampled-data control linear systems subject to uniform input quantization are considered. Within this context, the design of a stabilizing sampled-data state feedback controller is proposed. The proposed controller guarantees uniform global asymptotic stability of an attractor containing the origin of the plant. Due to the interplay of continuous-time dynamics and instantaneous changes in the state, the closed-loop system is modeled as a hybrid dynamical system. By relying on a quadratic clock-dependent Lyapunov function, sufficient conditions in the form of bilinear matrix inequalities are provided to ensure closed-loop stability. These conditions are employed to devise an optimal controller design algorithm based on the use of convex–concave decomposition approach. This leads to an iterative design algorithm based on the solution to a sequence of semidefinite programs for which feasibility is guaranteed. Some illustrative examples show the effectiveness of the proposed results.