Synchronization of Chaotic Neural Networks: Average-Delay Impulsive Control

In the brief, delayed impulsive control is investigated for the synchronization of chaotic neural networks. In order to overcome the difficulty that the delays in impulsive control input can be flexible, we utilize the concept of average impulsive delay (AID). To be specific, we relax the restriction on the upper/lower bound of such delays, which is not well addressed in most existing results. Then, by using the methods of average impulsive interval (AII) and AID, we establish a Lyapunov-based relaxed condition for the synchronization of chaotic neural networks. It is shown that the time delay in impulsive control input may bring a synchronizing effect to the chaos synchronization. Furthermore, we use the method of linear matrix inequality (LMI) for designing average-delay impulsive control, in which the delays satisfy the AID condition. Finally, an illustrative example is given to show the validity of the derived results.

Automated summary

This study investigates the use of delayed impulsive control for the synchronization of chaotic neural networks and proposes a method using average impulsive delay to overcome flexibility issues. By establishing relaxed conditions and utilizing linear matrix inequality for design, it was shown that time delay in impulsive control input can have a synchronizing effect. An illustrative example was used to demonstrate the validity of the results.