Mean square synchronization for stochastic delayed neural networks via pinning impulsive control

The mean square synchronization for a class of general stochastic delayed neural networks is explored in this paper using pinning impulsive control (PIC). It is evident that PIC combines the profits of pinning control and impulsive control. Considering that there is a time delay between the allocation and execution of impulsive instructions in practice, the idea of average impulsive delay (AID) is brought to describe this kind of delay. Furthermore, in actuality, neural networks with internal delay and stochastic disturbance are more general. Accordingly, some appropriate criteria are derived using the Lyapunov stability theory and the Fubini theorem to ensure mean square synchronization in two different cases, namely when the controller is designed with and without the impulsive delay. Finally, some numerical examples are afforded to validate the efficiency of theoretical results.