A study on the relationship between consensus of edge dynamics and node dynamics

In this paper, we examine the relationship between consensus of node dynamics and edge dynamics of a multi-agent system. The communication network topology of the multi-agent system is assumed to be a directed cyclic pursuit graph. We provide two linear forms of the edge dynamics. We show that if the node dynamics can reach a consensus, then the edge dynamics also reaches a consensus asymptotically. Finally, some simulation examples are presented to show the effectiveness of our theoretical results.