Additive Networks of Chen-Fliess Series: Local Convergence and Relative Degree

TL;DR

This paper investigates additive networks of systems modeled by Chen-Fliess series, establishing local convergence of input-output maps and conditions for well-defined relative degrees, showing these properties are generally typical.

Contribution

It provides new conditions ensuring local convergence and relative degree existence in additive Chen-Fliess networks, extending understanding of their structural properties.

Findings

Input-output maps have locally convergent Chen-Fliess series representations.

Conditions for the existence of a well-defined relative degree are established.

Relative degree property is shown to be generic in the network context.

Abstract

Given an additive network of input-output systems where each node of the network is modeled by a locally convergent Chen-Fliess series, two basic properties of the network are established. First, it is shown that every input-output map between a given pair of nodes has a locally convergent Chen-Fliess series representation. Second, sufficient conditions are given under which the input-output map between a pair of nodes has a well defined relative degree as defined by its generating series. This analysis leads to the conclusion that this relative degree property is generic in a certain sense.