Second order linear consensus protocols with irregular topologies and time delay

A methodology for the stability analysis of linear consensus protocols for groups of agents driven by second order dynamics is presented in this paper. It is assumed that the communication topologies are undirected and that the time delays incur between the agents are constant and uniform for all the channels. The proposed technique takes advantage of the general structure of consensus protocols that allows a decomposition of the characteristic equation in a set of factors, facilitating the stability analysis. The factors generated by this procedure are individually studied using the Cluster Treatment of Characteristic Roots paradigm, a recent method which declares the stability features of the system for various compositions of the time delay and other control parameters. Several illustrative examples are provided.