A Finiteness Criterion for Nonlinear Input–Output Differential Systems

Abstract

We solve the following problem which has been dealt with in several publications: when does a system have the same input–output behaviour as a system depending linearly on the state variables? Precise definitions of this question are supplied in the text. A particular case of the problem is the equivalence of a system with a bilinear one. At the end, we illustrate our methods and the scope of our results by a brief study of several examples.