Synchronization control for discrete-time complex dynamical networks with dynamic links subsystem

In this paper, the synchronization of discrete-time complex dynamical network with dynamic links is investigated. From the angle of large-scale system, if the links and nodes are time-varying, the complex dynamical network may be regarded to be composed of nodes subsystem (NS) and links subsystem (LS). The weighted value of links between nodes can be regarded as the state variables of LS, the above two subsystems are mutually coupled. The two subsystems are modeled mathematically by the state difference equations, especially, the dynamics of LS is modeled as Riccati matrix difference equation without control input. Different from the previous researches, this work concerns simultaneously the dynamics of LS and NS, by which the synchronization of NS is investigated. Associated with the given dynamic reference target for LS, the nodes controller is synthesized to ensure the state synchronization of NS to be achieved with the assistance of the LS. Finally, the numerical simulation is given to illustrate the effectiveness of the proposed theoretical results in this paper.