Necessary and sufficient conditions for the identifiability of isolated loops

TL;DR

This paper establishes simple, visual criteria for determining when the structure of a looped dynamical network can be uniquely identified from measurements and excitations, aiding network analysis.

Contribution

It provides the first necessary and sufficient conditions for loop network identifiability that are easy to verify visually.

Findings

Conditions are simple and can be checked visually.

All identifiable excitation and measurement patterns are characterized.

The criteria facilitate network identifiability analysis.

Abstract

This Letter provides necessary and sufficient conditions on the excitation and measurement pattern (EMP) that guarantee identifiability of a dynamical network that has the structure of a loop. The conditions are extremely simple in their formulation, and they can be checked by visual inspection. They allow one to easily characterize all EMPs that make the loop network identifiable.