Asymptotical Outer Synchronization for the Controlled Complex Dynamic Networks with Unknown Bounded Interaction

This paper investigates the problem of asymptotical outer synchronization for two complex dynamic networks (CDNs), one of which is called as the drive network and another is as the response network. Compared with the existing literature, the unknown bounded state interaction between the two CDNs is focused with the unknown and non-dissipative outer coupling configuration matrices of the drive-response networks, and thus the dynamic models of CDNs with interaction are proposed more general in structural form. Then, combined with the matrix analysis and Lyapunov stability methods, the relevant mathematical assumptions are proposed based on actual engineering background, with which the adaptive outer synchronization controller is synthesized in this paper. Therefore, the matrix straightening operation in the existing literature is avoided in this paper, which leads to the clearer structure of the designed controller. Finally, the effectiveness of the proposed method is verified by numerical simulation with the comparative example.