In this paper we study the feedback stabilization problem for the control-affine system x˙ =Ax +uBx The operator A is assumed to be the generator of a compact C 0 -semigroup of contractions in a separable complex Hilbert space H; B is a locally Lipschitz mapping on H. First, based on the decomposition of contraction semigroup, we present sufficient conditions for stabilization of the system by means of the feedback law u=−x, Bx. Second, we show that under general assumptions all solutions of the closed loop system are asymptotic to the set of equilibria E as t tends to infinity. This result offers sufficient conditions for global stabilization of the system at the origin. Finally, we consider the question of robustness of the above feedback law. In other words we show that the stability property of the system, with the same control law u=−x, Bx, remains invariant under certain classes of perturbations of the generator A.