Necessary and sufficient conditions for identifiability with partial excitation and measurement in linear dynamic networks

Determine necessary and sufficient conditions for the identifiability of linear dynamic networks, where dynamics are located at the edges, under partial excitation and partial measurement.

Background

The introduction contrasts well-understood identifiability results in linear networks with full excitation or full measurement against the less understood case where both excitation and measurement are partial. Although several conditions have been derived in recent literature, a complete necessary and sufficient characterization remains unresolved.

This open problem concerns linear networks in which edge dynamics are linear, a canonical setting in dynamical network identification. Resolving it would unify existing partial results and provide definitive guidance on sensor/actuator placement and network topology requirements for identifiability under realistic constraints.