Designing pinning network controllability for interdependent dynamical networks

This paper is concerned with a special type of controllability called pinning controllability of a general model of interdependent networks. In contrast to the conventional concept of synchronization, a new notion is developed for pinning control of intersection networks which are the resultant of follower-leader residual networks. Inherently appeared in the real networks, perfect synchronization is achieved such that the nodes within the clusters of the networks are synchronized with their corresponding leader nodes. In other words, the residual dynamics are satisfied to be exponentially converged as well as controllability guaranteed. Benefiting from impulsive control theory, this paper is focused on a global synchronization scheme. Given the corresponding Lipchitz conditions for the clusters and boundedness of the signals, sufficient conditions are obtained to ensure the globally exponentially stability criteria. A numerical validation of realistic chaotic interdependent networks with interdependency connectivity of power-law model is demonstrated to justify the theoretical results.