Finding the Exact Delay Bound for Consensus of Linear Multi-Agent Systems

This paper focuses on consensus problems for high-order, linear multi-agent systems. Undirected communication topologies and fixed, uniform communication time delay are taken into account. This class of problems has been widely study in the literature, but there are still gaps concerning the exact delay stability bounds in the domain of the delays. The more common analysis employed is based on Lyapunov-Krasowskii functionals, which produce very conservative results that are cumbersome to apply. As an alternative, we employ the Cluster Treatment of Characteristic Roots paradigm to study the stability of the system in the space of the delay. This allows the generation of exact and exhaustive delay bounds in an efficient manner. Before the stability analysis, a state transformation is performed to decouple the system and simplify the problem, as it was previously done for consensus problem of agents with simpler dynamics. Simulation results are presented to support the analytical claims.