Zeros of Networked Systems with Time-invariant Interconnections

TL;DR

This paper analyzes the zeros of networked linear systems with fixed interconnection structures, detailing how individual agent zeros and interconnection zeros influence the overall network zeros, especially in homogeneous cases.

Contribution

It provides a detailed characterization of zeros in homogeneous networked systems with time-invariant interconnections, linking individual and network zeros, and relating network zeros to blocked system versions.

Findings

Zeros of individual agents influence network zeros

Zeros of interconnection dynamics contribute to network zeros

Relationship established between network zeros and blocked system zeros

Abstract

This paper studies zeros of networked linear systems with time-invariant interconnection topology. While the characterization of zeros is given for both heterogeneous and homogeneous networks, homogeneous networks are explored in greater detail. In the current paper, for homogeneous networks with time-invariant interconnection dynamics, it is illustrated how the zeros of each individual agent's system description and zeros definable from the interconnection dynamics contribute to generating zeros of the whole network. We also demonstrate how zeros of networked systems and those of their associated blocked versions are related.