Coupled-group consensus seeking for second-order multi-agent systems with communication delay

This paper investigates the coupled-group consensus problem of second-order multi-agent systems subjected to communication delay, and we adopt a linear synchronously-coupled consensus protocol under the assumption that the sum of each agent´s adjacent weights to the agents in the other sub-group is zero in the interconnection topology. Based on Lyapunov-Krasovskii functional, delay-dependent sufficient consensus conditions formulated as Linear matrix inequalities (LMIs) are obtained for the system under fixed topology and switching topologies respectively. Simulation examples are given to verify the theoretical results.