Accelerating Consensus in High-Order Leader-Follower Networks

We consider the problem of accelerating the convergence to consensus of a network of homogeneous high-order agents, through the injection of an additional control input performed by a leader. After a brief set-up description, we derive the characteristic polynomial of the resulting system under the leader’s control. We introduce the concept of leader controlled distributed consensus, by imposing that the leader’s action improves the convergence speed but does not affect the consensus value, except possibly for a scaling factor. Finally, we prove that, under certain assumptions, consensus can be achieved with arbitrary speed.