Synchronization of hybrid-coupled delayed dynamical networks via aperiodically intermittent pinning control

In this paper, we concern the exponential synchronization problem for hybrid-coupled delayed dynamical networks via pinning aperiodically intermittent control. Different from previous works, the delayed coupling term considered here contains the transmission delay and self-feedback delay, and the intermittent control can be aperiodic. By establishing a new differential inequality and constructing Lyapunov function, several useful criteria are derived analytically to realise exponential synchronization for both free time delay (there is no restriction imposed on the delay and the control (and/or rest) width) and small time delay (the delay is smaller than the minimum of control width). Moreover, the detail of pinning and aperiodically intermittent control strategy are provided. Finally, a numerical example is given to demonstrate the validness of the proposed scheme.