Synchronisation of multiple neural networks via event‐triggered time‐varying delay hybrid impulsive control

Abstract

This article discusses the exponential synchronisation problem for multiple neural networks with time-varying delay and a more general non-Laplacian coupling matrix is considered. To reduce the redundant communication, two event-based time-varying delay hybrid impulsive control schemes are proposed with static event-triggered condition and dynamic event-triggered condition. These novel control schemes neatly combine the event-triggered coupling strategy with the time-varying delay hybrid impulsive control, where the impulsive instant is only determined by the specified event-triggered condition. Moreover, a delay impulsive differential inequality is established to discuss the synchronisation problem for controlled multiple neural networks. By using Stolz's theorem and introducing the average event-triggered delay impulsive gain, some less conservative sufficient conditions are derived to assure the stability of the time-varying delay multiple neural networks. Furthermore, the Zeno behaviour can be eliminated effectively and the consumption of the computing resources can be reduced. Finally, some examples are given to verify the superiority of the results. First, a static event-triggered time-varying delay hybrid impulsive control scheme was proposed to lessen the communication burden. Then, a time-varying delay impulsive differential inequality was established to guarantee the synchronisation of multiple neural networks. Moreover, the authors also discussed the issue that continuously triggering and sampling can be excluded.