On the Controllability Properties of Circulant Networks

This paper examines the controllability of a group of first order agents, adopting a weighted consensus-type coordination protocol over a circulant network. Specifically, it is shown that a circulant network with Laplacian eigenvalues of maximum algebraic multiplicity q is controllable from q nodes....

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Bibliographic Details
Published inIEEE transactions on automatic control Vol. 58; no. 12; pp. 3179 - 3184
Main Authors Nabi-Abdolyousefi, Marzieh, Mesbahi, Mehran
Format Journal Article
LanguageEnglish
Published New York IEEE 01.12.2013
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects
Circulant graphs
Controllability
coordination algorithms
Discrete Fourier transforms
Eigenvalues and eigenfunctions
Laplace equations
network controllability
Protocols
Symmetric matrices
Vectors
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Summary:This paper examines the controllability of a group of first order agents, adopting a weighted consensus-type coordination protocol over a circulant network. Specifically, it is shown that a circulant network with Laplacian eigenvalues of maximum algebraic multiplicity q is controllable from q nodes. Our approach leverages on the Cauchy-Binet formula, which in conjunction with the Popov-Belevitch-Hautus test, leads to new insights on structural aspects of network controllability.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2013.2259992