Leader-follower coherence in noisy ring-trees networks

Abstract

This paper investigates leader-follower network coherence in a noisy ring-trees network model with preassigned leaders at the initial state. Different from existing works on designing consensus algorithms in the multi-agent systems, the leader-follower coherence characterized by the eigenvalues of a principal submatrix obtained from the Laplacian matrix is a measure of deviation from the state of the leaders in an $$H_2$$ norm. The recursive properties of ring-trees networks allow analytical calculations of this network coherence. Based on the relationship of the eigenvalues of the submatrix in two successive steps, an analytical expression for the leader-follower coherence is determined depending on the number of leaders and network parameters. This network model shows better consensus with the increasing number of leaders in the ring network and the ring-trees topology has a profound impact on the coherence.