Two approaches for state space realization of NARMA models:: Bridging the gap

This paper studies the necessary and sufficient conditions for observable realization of a general class of nonlinear high-order input-output difference equations. In particular, it proves the equivalence of the two seemingly different existing approaches in the literature. The paper also provides a subclass of NARMA input-output models that are guaranteed to have an observable realization. It is shown that this class covers several important subclasses of existing NARMA models.