  Given a non-contracting trajectory of a nonlinear system, we consider the
question of designing an input perturbation that makes the perturbed trajectory
contracting. This paper stresses the analogy of this question with the
classical question of feedback stabilization. In particular, it is shown that
the existence of an output variable that ensures contraction of the inverse
system facilitates the design of a contracting input perturbation. We
illustrate the relevance of this question in parameter estimation.
