On the Controllability Properties of Circulant Networks
Marzieh Nabi-Abdolyousefi, Mehran Mesbahi · IEEE Transactions on Automatic Control · 2013
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.