Controllability of $\mathcal{N}$ -Duplication Corona Product Networks With Laplacian Dynamics

This article studies the controllability of a new composite network generated by two smaller scale factor networks via the Corona product with Laplacian dynamics. First, the eigenvalues and corresponding eigenvectors of a new composite network—the
$\mathcal{N}$
-duplication Corona product network—are derived by some properties of its factor networks. Second, a necessary and sufficient algebra-based criterion for the controllability of such network is established based on the Popov-Belevitch-Hautus (PBH) test. Furthermore, the weights on edges between the different factor networks are considered. Finally, several examples are presented to demonstrate the effectiveness of our results applied to the unmanned aerial vehicle (UAV) formation.