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Much recent research has dealt with the identifiability of a dynamicalnetwork in which the node signals are connected by causal linear time-invarianttransfer functions and are possibly excited by known external excitationsignals and/or unknown noise signals. So far all results on the identifiabilityof the whole network have assumed that all node signals are measured. Underthis assumption, it has been shown that such networks are identifiable only ifsome prior knowledge is available about the structure of the network, inparticular the structure of the excitation. In this paper we present the firstresults for the situation where not all node signals are measurable, under theassumptions that the topology of the network is known, that each node isexcited by a known signal and that the nodes are noise-free. Using graphtheoretical properties, we show that the transfer functions that can beidentified depend essentially on the topology of the paths linking thecorresponding vertices to the measured nodes. An important outcome of ourresearch is that, under those assumptions, a network can often be identifiedusing only a small subset of node measurements.

Identifiability of dynamical networks: which nodes need be measured?