Generalized Nyquist consensus condition for high-order linear multi-agent systems with communication delays

The generalized Nyquist criterion is used to derive necessary and sufficient consensus conditions for large high-order linear multi-agent systems (MAS) with heterogeneous communication delays. The new consensus conditions are set-valued graphical conditions, from which inequality conditions are derived for single integrator MAS. The obtained conditions provide a unification and generalization of several results from the literature. Moreover, convergence rate conditions for single integrator MAS with delays are derived.