Direct construction of minimal bilinear realizations from nonlinear input-output maps

The paper is concerned with the construction of bilinear state space descriptions from a prescribed nonlinear input-output map. The problem is shown to be equivalent to that of matching an infinite sequence of constant parameters which uniquely identifies the given map. Both the problems of requiring the matching over a finite number of terms of the sequence (partial realization problem) and over the whole sequence (complete realization problem) are treated. In both cases explicit existence criteria and an algorithm for finding minimal realizations are given. The approach is based on the introduction of a suitable infinite matrix formed with the input-output parameters, which can be considered as a generalization of the Hankel matrix usually considered in the realization theory of linear systems.