A two-layer transformation for characterizing the zeros of a network input-output dynamics

Many networks can be modeled as collections of subsystems with complex internal dynamics, which are dynamically coupled according to a weighted digraph. This article characterizes the input-output behavior of a network of coupled homogeneous single-input single-output subsystems, in the case where external actuation and measurement are each applied at a single (but possibly different) component. Precisely, a two-layer transformation of the network´s dynamics is undertaken, which makes explicit the roles of 1) the local subsystem model, 2) the network´s global interconnections (graph), and 3) the input and output locations, in determining the zeros of the input-output model. The analysis of the zeros via this special-coordinate-basis decomposition shows a parallel with the spectral analysis of the coupled-subsystem model, and directly gives insight into the network´s input-output dynamics and its feedback control.