$H_{\infty }$ Weighted Integral Event-Triggered Synchronization of Neural Networks With Mixed Delays

This article considers an event-triggered H
_∞
synchronization of neural networks (NNs) with mixed (discrete and distributed) delays. To release the communication burden, a novel weighted integral event-triggered scheme (IETS) is proposed based on the past information of the system dynamics. In this scheme, for the first time, a weighting function is proposed to weight the system state over a given period, which can be viewed as a forgetting factor. Moreover, a waiting time interval is added in the proposed IETS to exclude Zeno phenomenon. By constructing a novel Lyapunov-Krasovskii functional with the distributed delay kernel and the weighting function, sufficient linear matrix inequality conditions for the existence of an event-triggered controller that guarantees an exponential synchronization of the delayed NNs with an H
_∞
performance are derived. Finally, an illustrative example and an application to image encryption are used to demonstrate the advantage of the proposed approach.