The Observability Radius of Networks

Paolo Frasca, Gianluca Bianchin, Andrea Gasparri

    Research output: Contribution to journalArticleAcademicpeer-review

    16 Citations (Scopus)
    4 Downloads (Pure)


    This paper studies the observability radius of network systems, which measures the robustness of a network to perturbations of the edges. We consider linear networks, where the dynamics are described by a weighted adjacency matrix and dedicated sensors are positioned at a subset of nodes. We allow for perturbations of certain edge weights with the objective of preventing observability of some modes of the network dynamics. To comply with the network setting, our work considers perturbations with a desired sparsity structure, thus extending the classic literature on the observability radius of linear systems. The paper proposes two sets of results. First, we propose an optimization framework to determine a perturbation with smallest Frobenius norm that renders a desired mode unobservable from the existing sensor nodes. Second, we study the expected observability radius of networks with given structure and random edge weights. We provide fundamental robustness bounds dependent on the connectivity properties of the network and we analytically characterize optimal perturbations of line and star networks, showing that line networks are inherently more robust than star networks.
    Original languageEnglish
    Pages (from-to)3006 - 3013
    Number of pages7
    JournalIEEE transactions on automatic control
    Issue number6
    Publication statusPublished - 6 Jun 2017


    • The Observability
    • Radius of Networks
    • n/a OA procedure


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