Transfer functions in consensus systems with higher-order dynamics and external inputs

TL;DR

This paper analyzes transfer functions in consensus systems with higher-order agent dynamics and external inputs, revealing explicit structures that connect network topology with agent behavior and controllability.

Contribution

It provides a unified product form for transfer functions in directed graphs with higher-order agents, linking system dynamics to network properties and controllability.

Findings

Transfer functions have a simple product form combining network and agent dynamics.

The link between higher-order and single-integrator systems is established.

Graph properties determine the minimal controllable subspace dimension.

Abstract

This paper considers transfer functions in consensus systems where agents have identical SISO dynamics of arbitrary order. The interconnecting structure is a directed graph. The transfer functions for various inputs and outputs are presented in simple product forms with a similar structure of the numerator and the denominator. This structure combines the network properties and the agent model in an explicit way. The link between a higher-order and a single-integrator dynamics is shown and the polynomials of the transfer function in the single-integrator system are related to the graph properties. These properties also allow to generalize a result on the minimal dimension of the controllable subspace to the directed graphs.