On reaching group consensus for linearly coupled multi-agent networks

In this paper, the problems of group consensus for linearly coupled multi-agent networks including first-order and second-order are investigated, respectively. Based on the Laplacian matrix associated with the weighted adjacency matrix of the system, we present two novel linear protocols which can exactly reflect the interactive influence between the agents of the multi-agent network. Instead of relying on other conservative assumptions presented by the majority of the relevant research works, some promising criteria which can guarantee the reaching of group consensus of the multi-agent network are also obtained analytically. In addition, we also extend our work to study the group consensus for the multi-agent network with generally connected topology which neither needs to be strongly connected nor needs to contain a directed spanning tree. The conclusion that we have obtained should be more representative. Finally, the validity and correctness of our theoretical results are verified by several numerical simulated examples.