Dynamical Structure Functions for the Estimation of LTI Networks with Limited Information

This research explores the role and representation of network structure for LTI Systems. We demonstrate that transfer functions contain no structural information without more assumptions being made about the system, assumptions that we believe are unreasonable when dealing with truly complex systems. 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. We use Dynamical Structure to prove necessary and sufficient conditions for estimating structure from data, and demonstrate, for example, the danger of attempting to use steady-state information to estimate network structure.