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

TL;DR

This paper derives exact and efficient delay bounds for the stability of consensus in high-order linear multi-agent systems with fixed communication delays, improving over conservative Lyapunov-based methods.

Contribution

It introduces a novel approach using the Cluster Treatment of Characteristic Roots to obtain precise delay bounds for complex multi-agent systems.

Findings

Exact delay bounds are computed efficiently.

The method outperforms traditional Lyapunov-Krasowskii approaches.

Simulation validates the analytical results.

Abstract

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.