Controllability of Symmetric Double Layer Networks

This paper mainly considers the controllability of a class of symmetric double-layer networks (SDLNs) with inter-layer undirected connections, inter-layer directed connections and inter-layer random connections. The eigenvalues and eigenvectors of the super-Laplacian matrix of the SDLNs can be derived from eigenvalues and eigenvectors of the factor networks, and based on the PBH test, some sufficient or necessary conditions for the controllability of the SDLNs can be obtained through the controllability of the factor networks with a new control strategy. Furthermore, several examples and simulations are provided to validate the accuracy of the obtained results.