# Topological Controllability of Undirected Networks of Diffusively-Coupled Agents

## TL;DR

This paper develops new topological controllability conditions for undirected networks of diffusively coupled agents, focusing on edge signs rather than connectivity, and introduces methods for graph merging and decomposition to assess controllability.

## Contribution

It introduces a novel approach to topological controllability based on edge signs and provides graph merging and decomposition techniques for analysis.

## Key findings

- Provides conditions for controllability based on edge signs.
- Introduces a process for merging controllable graphs.
- Develops a graph decomposition method for controllability evaluation.

## Abstract

This paper presents conditions for establishing topological controllability in undirected networks of diffusively coupled agents. Specifically, controllability is considered based on the signs of the edges (negative, positive or zero). Our approach differs from well-known structural controllability conditions for linear systems or consensus networks, where controllability conditions are based on edge connectivity (i.e., zero or nonzero edges). Our results first provide a process for merging controllable graphs into a larger controllable graph. Then, based on this process, we provide a graph decomposition process for evaluating the topological controllability of a given network.