A Framework of Stability Analysis for Multi-agent Systems on Arbitrary Topology Graph: Linear Systems

TL;DR

This paper introduces a novel stability analysis method for linear multi-agent systems that is topology-independent, focusing on input-output relationships and recursive graph construction, enabling analysis on any network structure.

Contribution

It presents a new stability analysis framework that treats agents as isolated units and simplifies graph construction, differing from traditional Laplacian and Lyapunov methods.

Findings

Applicable to arbitrary topology graphs

Recursive stability analysis procedure

Independent of specific network structures

Abstract

In this paper, from the structural perspective, we propose a new stability analysis approach for the consensus of linear multi-agent systems. Different from the general tools: the Laplacian matrix based method and the Lyapunov's method, this approach treats the multi-agent system as the composition of many isolated agents, and focuses on their special input and output relationship. Through transforming the construction of a graph into a standard procedure only including three basic structures, the stability analysis is recursive and independent of the specific topology. Therefore, this approach can be used for multi-agent systems on any topology graph.