Dynamical Structure Functions for the Reverse Engineering of LTI Networks

Abstract — This research explores the role and representation of network structure for LTI systems with partial state observations. We demonstrate that input-output representations, i.e. transfer functions, contain no internal structural information of the system. We further show that neither the additional knowledge of system order nor minimality of the true realization is generally sufficient to characterize network structure. We then introduce dynamical structure functions as an alternative, graphical-model based representation of LTI systems that contain both dynamical and structural information of the system. The main result uses dynamical structure to precisely characterize the additional information required to obtain network structure from the transfer function of the system. I