Cluster anti-consensus in directed networks of multi-agents based on the Q-theory

In this paper, we investigate the cluster anti-consensus problem for multi-agent systems with directed information exchange. The algebra graph theory is reviewed and the properties of signless Laplacian matrix of a directed graph are derived. Then a new control protocol is designed to achieve cluster anti-consensus of multi-agent systems based on the Q-theory. Sufficient conditions are given to guarantee the cluster anti-consensus of multi-agent systems by using the properties of signless Laplacian matrix. Numerical simulations show the effectiveness of our theoretical results.