  This paper addresses the problem of identifying the graph structure of a
dynamical network using measured input/output data. This problem is known as
topology identification and has received considerable attention in recent
literature. Most existing literature focuses on topology identification for
networks with node dynamics modeled by single integrators or single-input
single-output (SISO) systems. The goal of the current paper is to identify the
topology of a more general class of heterogeneous networks, in which the
dynamics of the nodes are modeled by general (possibly distinct) linear
systems. Our two main contributions are the following. First, we establish
conditions for topological identifiability, i.e., conditions under which the
network topology can be uniquely reconstructed from measured data. We also
specialize our results to homogeneous networks of SISO systems and we will see
that such networks have quite particular identifiability properties. Secondly,
we develop a topology identification method that reconstructs the network
topology from input/output data. The solution of a generalized Sylvester
equation will play an important role in our identification scheme.
