  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.
