Controllability of Cartesian Product Signed Networks

A necessary and sufficient algebraic condition is obtained for the controllability of a composite signed network consisting of two factor networks by Cartesian product, which reveals how the controllability of the higher-dimensional Cartesian product network is affected by the controllability of its smaller-scale low-dimensional factor networks. Furthermore, the structural balance of the Cartesian product network can be judged by the structural balance of its factor networks, which can greatly reduce amount of calculation to some extent. And the agents’ state evolution trajectories of Cartesian product networks can also be predicted by those of their factor networks. Moreover, the controllability of general signed networks is considered. Algorithms and numerical examples are exhibited to demonstrate the validity of our methods.