Existence of global input-output model for nonlinear systems

The existence of input-output model is essential for identification and control problems since many prediction and control techniques are based upon the input-output representations rather than state-space models. For linear time-invariant system, it is well known that the input-output model exists, which is called the ARMA (auto-regressive moving average) model. For nonlinear systems, it was also established that the ARMA model can be extended locally around the origin, which is called the NARMA (i.e., nonlinear ARMA) model. In this paper, some recent results on the extensions of these ideas to global input-output representation for general discrete-time nonlinear systems will be presented. It is proven by transversality theory from differential topology that global input-output model exists for almost every nonlinear system.