Hierarchical consensus for multi-agent systems with low-rank interconnection

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 interconnection matrix which expresses interconnection property between layers, where we focus on the rank of this matrix. In order to examine the relationship between the rank of interconnection matrix and stability degree of the system, we analytically derive the eigenvalue distribution of the system 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.