Outer Synchronization for Multi-derivative Coupled Complex Networks with and without External Disturbance

This paper investigates the outer synchronization of multi-derivative coupled complex networks (MDCCNs), and further studies the outer \(H_{\infty }\) synchronization between two MDCCNs with external disturbance. For the outer synchronization, a synchronization criterion is proposed by using adaptive control strategy, which is proved based on Lyapunov functional and the Barbalat’s lemma. For the outer \(H_\infty \) synchronization, an adaptive state controller and parameter updating scheme are devised for MDCCNs with external disturbance. Finally, the validity of the presented criteria is demonstrated by providing two simulation examples.