  Stability and stabilization for linear state feedback control systems in the
presence of sensor quantization 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 solution to the considered
problems are illustrated. The effectiveness of the proposed methodology is
shown in three examples.
