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On the Controllability Properties of Circulant Networks

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2 Author(s)
Nabi-Abdolyousefi, M. ; Palo Alto Res. Center (PARC), Xerox Co., Palo Alto, CA, USA ; Mesbahi, M.

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.

Published in:

Automatic Control, IEEE Transactions on  (Volume:58 ,  Issue: 12 )