Aggregation of dynamical agents in network

This paper investigates the aggregation of dynamical agents in network. The communication topology of network is characterized by a undirect graph and the agents are Lyapunov stable distributed in a plane. We provide with the conditions under which the group of agents will achieves gradually aggregation. Numerical simulations show that our theoretical results are effective. By comparison with the former works on this topic, e.g., our study shows that when the dynamic agents is moving in a plane the aggregation condition is very different from that in a line. The stability conditions depend not only on the control protocol, but also on the eigenvalues of graph Laplacian associated with the network, as well as the dynamical behaviors of agents. Whereas for the agents moving in a line the aggregation stability condition depends on the control protocol only.