Stability and stabilization for linear state feedback control systems in the presence of sensor quantiza- tion are studied. As the closed-loop system is described by a discontinuous right-hand side differential equation, Krasovskii solutions (to the closed-loop system) are considered. Sufficient conditions in the form of matrix inequalities are proposed to characterize uniform global asymptotic stability of a compact set containing the origin. Such conditions are shown to be always feasible whenever the quantization free closed-loop system is asymptotically stable. Building on the obtained conditions, computationally affordable algorithms for the solutions to the considered problems are illustrated. The effectiveness of the proposed methodology is shown in three examples.