Stability of a Consensus Protocol for Second Order Agents With Multiple Time Delays Available to Purchase

In this study we consider the consensus problem for a group of second order agents interacting under a fixed, undirected communication topology. Communication lines are affected by two rationally independent delays. The first delay is assumed to be in the position information channels whereas the second one is in the velocity information exchange. The delays are assumed to be uniform throughout the entire network. We first reduce the complexity of the problem, by performing a state transformation that allows the decomposition of the characteristic equation of the system into a set of second order factors. The stability of the resulting subsystems is analyzed exactly and exhaustively in the domain of the time delays using the Cluster Treatment of Characteristic Roots (CTCR) paradigm. CTCR is a recent method which declares the stability features of the system for any composition of the time delays. Example cases are provided to verify the analytical conclusions.