On the zeros of consensus networks

In this paper, we focus on the signal transfer between any two agents in a consensus network and provide an analysis of the resulting transfer function and transmission zeros. Our contributions include relating the distance between the input and output node to the relative degree of the system and showing that the gain factor of the transfer function is equal to the number of shortest paths between the two nodes. We show that for certain input-output configurations, the zeros interlace with the poles. Bounds on the zero locations and minimum phase properties of certain graph and input-output configurations are provided.