A note on the structural functional observability problem

The functional observability problem deals with the possibility to estimate a linear combination of the states of a system, even if the system is not observable. This is a classical problem in control theory, which was recently revisited in several papers in the context of network theory, leading to the notion of structural functional observability. The objective of this note is to prove that the dual of structural functional observability problem is closely related with the notion of fixed controllable subspace in a structured system. This observation allows another interesting characterization of structural functional observability. This characterization has also an interest for efficiently solving the structural functional observability problem.