Distributed Synchronization of Delayed Neural Networks: Delay-Dependent Hybrid Impulsive Control

In this paper, synchronization of coupled neural networks is investigated via distributed delayed impulsive control, and system delays, coupling delays and impulsive delays are simultaneously considered. Firstly, the concept of average delayed impulsive weight is proposed, which allows impulsive weights and impulsive delays to be integrated into just one expression, and afterward hybrid impulses can be augmented. Then, this paper extends the comparison principle by taking delayed impulses into account, where the limitation that system delays exist between two consecutive impulsive instants is released. Without any restriction on time delays, sufficient conditions of global exponential synchronization for coupled neural networks are obtained. Additionally, the corresponding convergence rate is estimated. It indicates that the networks can still achieve synchronization even if the impulses work negatively, or may destroy synchronization. Finally, three typical networks are investigated to verify the availability of the control schemes.