The main theorem states that if a nonlinear system
can be made globally asymptotically stable by a smooth feedback
, then there also exists a smooth feedback
such that the feedback modified system is input-to-state stable. The construction of
is given explicitly for feedback linearizable systems, which are trivially smoothly stabilizable. Based upon this main result it is also shown that smoothly stabilizable systems admit coprime factorizations. Finally some results about input-to-output stability are given.