DocumentCode
34847
Title
On the Controllability Properties of Circulant Networks
Author
Nabi-Abdolyousefi, Marzieh ; Mesbahi, Mehran
Author_Institution
Palo Alto Res. Center (PARC), Xerox Co., Palo Alto, CA, USA
Volume
58
Issue
12
fYear
2013
fDate
Dec. 2013
Firstpage
3179
Lastpage
3184
Abstract
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.
Keywords
Laplace equations; controllability; eigenvalues and eigenfunctions; Cauchy-Binet formula; Laplacian eigenvalues; Popov-Belevitch-Hautus test; algebraic multiplicity; circulant networks; controllability properties; first order agents; network controllability; Controllability; Discrete Fourier transforms; Eigenvalues and eigenfunctions; Laplace equations; Protocols; Symmetric matrices; Vectors; Circulant graphs; coordination algorithms; network controllability;
fLanguage
English
Journal_Title
Automatic Control, IEEE Transactions on
Publisher
ieee
ISSN
0018-9286
Type
jour
DOI
10.1109/TAC.2013.2259992
Filename
6507614
Link To Document