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.