Cyclic pursuit behavior for hierarchical multi-agent systems with low-rank interconnection

This paper is concerned with the stability degree of a class of hierarchical multi-agent systems based on a fairly general model which expresses an integrated hierarchical systems by focusing on the rank of interconnection matrix. We first define the expression of the interconnection matrix and explain the significance of its low-rank property instead of sparseness or small gain property to represent the weakness of the interaction. We then derive the analytical eigenvalue distribution for a class of rank one interconnection matrix and examine the stability degree of the whole system for cyclic pursuit, which are confirmed by numerical examples with simulations. We also investigate the properties of rank two case is a preliminary step of the general case.