Implications of a dynamical-network´s graph on the estimability of its modes

The estimation of the modes of a linear dynamical network (specifically, a network synchronization process) is considered. We study pole/eigenvalue estimation when the network dynamics is subject to impulsive stimulation at one location, and time-course measurements are taken at a subset of network locations. We develop several characterizations of mode estimation performance, as indicated by the Cramér-Rao bound matrix, in terms of the eigenstructure and graph topology of the network. These results 1) allow comparison of the single- and multiple- observation cases, 2) provide structural bounds for particular graph classes (like planar and tree graphs), and 3) inform sensor placement.