Minimal realization of nonlinear systems described by input-output difference equations

In this paper, we consider a general class of nonlinear discrete-time syste ms described by their input-output (I/O) relationship. We first present the necessary and sufficient conditions for existence of a local observable st ate-space realization of the system and an explicit algorithm for computing it. In cases where the I/O map and its resulting realization are nonminima l, we formulate an algorithm for extracting its minimal realization wheneve r possible, The developed theory and algorithms are illustrated by means of several example.