Cluster-delay consensus in first-order multi-agent systems with nonlinear dynamics

In this paper, a new concept of cluster-delay consensus is defined, which means that all agents in the same cluster reach identical consensus and that any two agents in the different clusters reach delay consensus simultaneously. In fact, cluster-delay consensus is a kind of dynamics between identical consensus and cluster consensus. And then, the problem of leader-following cluster-delay consensus in a nonlinear multi-agent system is investigated. By using graph theory, Lyapunov stability theory and matrix theory, a control protocol for cluster-delay consensus is given, which is based on intrinsic dynamics of each agent and the topology of multi-agent system. Finally, some numerical simulations are also given to verify the theoretical analysis.