Abstract |
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—Much recent research has dealt with the identiﬁability of a dynamical network in which the node signals are connectedbycausallineartime-invarianttransferfunctionsand are possibly excited by known external excitation signals and/or unknown noise signals. So far all results on the identiﬁability of the whole network have assumed that all node signals are measured. Under this assumption, it has been shown that such networks are identiﬁable only if some prior knowledge is available about the structure of the network, in particular the structure of the excitation. In this paper we present the ﬁrst results for the situation where not all node signals are measurable, under the assumptions that the topology of the network is known, that each node is excited by a known signal and that the nodes are noise-free. Using graph theoretical properties, we show that the transfer functions that can be identiﬁeddependessentiallyonthetopologyofthepathslinking thecorrespondingverticestothemeasurednodes.Animportant outcome of our research is that, under those assumptions, a network can often be identiﬁed using only a small subset of node measurements. |