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A Global Identifiability Condition for Consensus Networks with Tree Graphs

In this paper we present a sufficient condition that guarantees identifiability of linear network dynamic systems exhibiting continuous-time weighted consensus protocols with acyclic structure. Each edge of the underlying network graph $\mathcal G$ of the system is defined by a constant parameter, referred to as the weight of the edge, while each node is defined by a scalar state whose dynamics evolve as the weighted linear combination of its difference with the states of its neighboring nodes. Following the classical definitions of identifiability and indistinguishability, we first derive a condition that ensure the identifiability of the edge weights of $\mathcal G$ in terms of the associated transfer function. Using this characterization, we propose a sensor placement algorithm that guarantees identifiability of the edge weights. We describe our results using several illustrative examples.