Node-to-node consensus of networked agents with general linear node dynamics

The concept of node-to-node consensus is introduced and discussed in this paper. Unlike most of the existing literature which focuses on designing distributed protocols to guarantee the states of all agents to converge to the same, the coordination goal in the present framework is to employ some distributed control laws such that each follower can track its corresponding leader while the whole system may not achieve consensus. It is assumed that there are two levels in the considered multi-agent systems, that is, the leader's and the follower's levels. Furthermore, the dynamics of each leader may only be affected by those of its neighbors in the leader's level while the dynamics of each follower may be affected by those of its neighbors in both leader's and follower's levels. To achieve node-to-node consensus, an algorithm is provided to determine what kinds of and how many followers should directly sense their corresponding leaders. Theoretical analysis indicates that the node-to-node consensus can be ensured if a fraction of followers suitably selected can sense their corresponding leaders and the inner linking matrix as well as the coupling strength are appropriately designed. Numerical simulations are finally given for illustration.