Lag H_∞ synchronization and lag synchronization for multiple derivative coupled complex networks

This paper mainly devotes to the study of lag H_∞ synchronization and lag synchronization issues for the multiple derivative coupled complex networks (MDCCNs) with and without external disturbances, which have never been investigated. On one side, with the help of state feedback controller, adaptive state feedback controller and Lyapunov functionals, two criteria are developed to insure the lag H_∞ synchronization for the MDCCN with external disturbances. On the other side, we also discuss the lag synchronization in the MDCCN in virtue of choosing appropriate state feedback controller and adaptive state feedback controller. Lastly, two numerical examples are put forward to verify the lag H_∞ synchronization and lag synchronization criteria.