Couple-group consensus conditions for general first-order multiagent systems with communication delays

In this paper, we establish group consensus conditions for first-order systems with communication delays using the relationship between time-delay parameter and the closed-loop characteristic roots. At first, we derive necessary conditions for the delay-free case, then we proceed to the delay-induced case. Contrary to most studies on group consensus where the conditions are derived considering the Laplacian of the entire multiagent network, we derive the group consensus conditions based on the Laplacian matrices that describe each subgroup and the inter-connection among sub-groups. Simulation studies are used to validate the derived conditions.