On the Inherent Integration Structure of Nonlinear Systems

Abstract

In this paper we characterize the inherent integration structure of affine nonlinear systems through a set of indices called—in analogy with existing terminology for linear systems—the orders of the zeros at infinity. We show that our definition encompasses earlier characterizations due to Hirschorn and Isidori. The discussion is entirely local in nature, so that we are able to use recent results in the ‘geometric approach’ to nonlinear system theory.