Stabilization of interdependent networks with two sub-networks of non-identical nodes

This paper explores the stabilization of interdependent networks comprising two sub-networks with non-identical nodes, in which one of the sub-networks is connected to the other in one-to-many mode. Firstly, we establish a mathematical model where the sub-networks possess different number of nodes. Besides, the outer coupling matrix is not required to satisfy the diffusive coupling condition. Then, based on some useful assumptions, adaptive decentralized controllers are designed to realize asymptotic stabilization of the system, the validity of the proposed controllers is rigorously established using Lyapunov stability methods. Finally, their effectiveness is demonstrated through two simulation examples.