Stabilizability, I/O stability and coprime factorizations

Coprime right factorizations are shown to exist for the input to state mapping of a continuous-time nonlinear system, provided that the smooth feedback stabilization problem be solvable for this system. As a particular case, it follows that feedback linearizable systems admit such factorizations. In order to establish this result, a Lyapunov-theoretic definition is proposed for bounded-input-bounded-output stability. The notion of stabilizability as studied in the state space nonlinear control literature is related to a notion of stability under bounded control perturbations analogous to those studied in operator-theoretic approaches to systems