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

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.

Automated summary

This paper studies the fixed-time synchronization problem of complex-valued coupled networks with hybrid perturbations. A novel quantized controller is designed to overcome the difficulties caused by complex parameters, variables, and disturbances. By using the Lyapunov stability theorem and properties of the Wiener process, sufficient conditions are provided for selecting control parameters to achieve fixed-time synchronization, and an upper bound for the setting time is obtained. Numerical simulations confirm the theoretical results and effectiveness of the control strategy.