Robust H∞ Pinning Synchronization for Complex Networks With Event-Triggered Communication Scheme

This paper investigates the issue of global robust <inline-formula> <tex-math notation="LaTeX">${H_\infty }$ </tex-math></inline-formula> pinning synchronization for a class of complex networks with sampled-data-based event-triggered communication via a pinning control approach. The complex network is subject to network-induced time-varying delays, parametric uncertainties and external disturbances. A directed and weighted communication topology is taken into account, and the phenomenon of uncertainties is reflected in both modelling and inner coupling matrices. In order to save communication resources, a new and practical event-triggered communication mechanism with an asynchronous sampling manner is developed, with which the Zeno behaviour can be absolutely avoided. Then, based on the presented event-triggered strategy, a pinning control protocol is proposed to reduce the frequency of controller updates and the computational burden. The problems on the minimal number and which of the nodes should be chosen are addressed. By Lyapunov stability theory, sufficient conditions are deduced to ensure the underlying network achieves global robust <inline-formula> <tex-math notation="LaTeX">${H_\infty }$ </tex-math></inline-formula> pinning synchronization. Finally, numerical examples are provided to verify the effectiveness of the new design techniques.