Extending identifiability results from isolated networks to embedded networks

This paper deals with the design of Excitation and Measurement Patterns (EMPs) for the identification of dynamical networks, when the objective is to identify only a subnetwork embedded in a larger network. Recent results have shown how to construct EMPs that guarantee identifiability for a range of networks with specific graph topologies, such as trees, loops, or Directed Acyclic Graphs (DAGs). However, an EMP that is valid for the identification of a subnetwork taken in isolation may no longer be valid when that subnetwork is embedded in a larger network. Our main contribution is to exhibit conditions under which it does remain valid, and to propose ways to enhance such EMP when these conditions are not satisfied.