Output Discernibility of Topological Variations in Linear Dynamical Networks

The conditions under which topological variations in networked linear dynamical systems can be discerned from their outputs are investigated. The output-indiscernible space is completely characterized without conditions imposed on the topology matrix. It is demonstrated that a topological change can be output-indiscernible even if the original and the altered topology matrices share no common eigenvalues. Furthermore, the necessary and sufficient condition for output discernibility is proposed, which is based on the observation matrix and the Jordan chains of the topology matrices. Additionally, a necessary condition distinct from discernibility conditions and two sufficient conditions for easy verification are derived. Examples on consensus dynamics are provided, highlighting the potential of our results in guiding sensor node allocation and initial value selection for detecting topological changes.