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

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.