Construction and Analysis of Inter-couplings for the Structural Controllability of Interdependent Networks

In this paper, we construct the inter-couplings and analyze the structural controllability of interdependent networks with known directed subnets. Firstly, we divide the interdependent network into a leader-system and a follower-system. The leader-system is proved to be certainly controllable, so we focus on constructing inter-couplings between two follower-subsystems and analyzing the structural controllability of the follower-system when the positions and the number of the leaders are fixed. Secondly, based on Kalman rank criterion, PBH rank criterion, as well as the graph maximum matching algorithm, combined with the controllable structure decomposition algorithm, several sufficient or necessary conditions for the structural controllability of the topological isomorphic follower-system are proposed to guarantee whether the follower-system and interdependent network are controllable or not. All the conditions provided in this paper also are suitable for the networks with undirected subnets. Finally, we take two examples to illustrate the feasibility and effectiveness of our theoretical conclusions.