Abstract
This paper deals with a hierarchical consensus problem in large scale systems. We first define the hierarchical consensus and propose a fairly general model of the system. We then define the incidence matrix which expresses interconnection property between layers, where we focus on the rank of the matrix. In order to examine the relationship between the rank of inter-layer incidence matrix and consensus performance, we analytically derive the eigenvalue distribution of the sysytem matrix in the case of circulant incidence matrix. The resultant distribution shows that the low-rank interconnection leads to the faster consensus in terms of rate of convergence and damping, which is confirmed by numerical examples with simulations.
