A Scalable Approach for Consensus Stability Analysis of a Large-Scale Multi-Agent System with Single Delay

This note presents a scalable approach for consensus stability analysis of a general class of large-scale Multi-Agent System (MAS) with single delay considering directed and undirected graphs. It is shown that, under certain conditions satisfied by several protocols reported in the literature, consensus in MAS can be ensured by studying a set comprising a small number of quasipolynomials of reduced complexity. Specifically, if the graph is undirected, it suffices to guarantee the stability of only two quasipolynomials in the set. If the graph is directed, then the set consists of a family of quasipolynomials, possibly two as well, associated with a polytope enclosing the eigenvalues of a Laplacian-like matrix. The approach renders the number of agents in the network irrelevant for consensus stability analysis as illustrated using two consensus protocols borrowed from the literature.