The stabilization problem of aperiodic sampleddata linear systems subject to input constraints is dealt with. A state feedback control law is designed to optimize the size of a polyhedral estimate of the region of attraction of the origin (RAO) of the closed-loop system. The control law is derived from the computation of a controlled contractive polytope for the dynamics between two successive sampling instants. The polytope is of low complexity as its number of vertices is fixed a priori. As shown in the numerical example, the polyhedral estimate of the RAO associated with the proposed feedback control is larger than the ones obtained with other approaches in the literature.