  We show that any globally asymptotically controllable system on any smooth
manifold can be globally stabilized by a state feedback. Since we allow
discontinuous feedbacks, we interpret the solutions of our systems in the
``sample and hold'' sense introduced by Clarke-Ledyaev-Sontag-Subbotin (CLSS).
Our work generalizes the CLSS Theorem which is the special case of our result
for systems on Euclidean space. We apply our result to the input-to-state
stabilization of systems on manifolds relative to actuator errors, under small
observation noise.
