Controllability-Gramian submatrices for a network consensus model

Principal submatrices of the controllability Gramian and their inverses are examined, for a network-consensus model with inputs at a subset of network nodes. Several properties of the Gramian submatrices and their inverses – including dominant eigenvalues and eigenvectors, diagonal entries, and sign...

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Bibliographic Details
Published inSystems & control letters Vol. 136; p. 104575
Main Authors Roy, Sandip, Xue, Mengran
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.02.2020
Subjects
Controllability and target controllability
Gramian
Network consensus
Security
Gramian
Controllability and target controllability
Security
Network consensus
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Summary:Principal submatrices of the controllability Gramian and their inverses are examined, for a network-consensus model with inputs at a subset of network nodes. Several properties of the Gramian submatrices and their inverses – including dominant eigenvalues and eigenvectors, diagonal entries, and sign patterns – are characterized by exploiting the special doubly-nonnegative structure of the matrices. In addition, majorizations for these properties are obtained in terms of cutsets in the network’s graph, based on the diffusive form of the model. The asymptotic (long time horizon) structure of the controllability Gramian is also analyzed. The results on the Gramian are used to study metrics for target control of the network-consensus model.
ISSN:0167-6911
1872-7956
DOI:10.1016/j.sysconle.2019.104575