Fixed-Time Synchronization of Complex-Valued Coupled Networks with Hybrid Perturbations via Quantized Control

Abstract

This paper considers the fixed-time synchronization of complex-valued coupled networks (CVCNs) with hybrid perturbations (nonlinear bounded external perturbations and stochastic perturbations). To accomplish the target of fixed-time synchronization, the CVCNs can be separated into their real and imaginary parts and establish real-valued subsystems, a novel quantized controller is designed to overcome the difficulties induced by complex parameters, variables, and disturbances. By means of the Lyapunov stability theorem and the properties of the Wiener process, some sufficient conditions are presented for the selection of control parameters to guarantee the fixed-time synchronization, and an upper bound of the setting time is also obtained, which is only related to parameters of both systems and the controller, not to the initial conditions of the systems. Finally, a numerical simulation is given to show the correctness of theoretical results and the effectiveness of the control strategy.

Fixed/Preassigned-Time Synchronization of Fully Quaternion-Valued Cohen–Grossberg Neural Networks with Generalized Time Delay

“…In order to address this challenge, the concept of fixed time (FIT) was introduced and the FIT stability theorem was first proposed in [17], in which the estimate of the ST is improved by eliminating its dependence on initial values. Since then, numerous remarkable research endeavors have emerged, encompassing FIT synchronization of recurrent neural networks [18][19][20], complex-valued neural networks (CVNNs) [21][22][23], and QVNNs [24][25][26][27][28]. In [24][25][26], the FIT synchronization of QVNNs was investigated by decomposing the QVNN model into four real valued neural networks, which resulted in four real-valued controllers being designed.…”