Predefined-Time Synchronization of Complex Networks with Disturbances by Using Sliding Mode Control

This paper aims to investigate the issue of predefined-time synchronization in complex networks with disturbances using sliding mode control technology. Firstly, a new predefined-time stability lemma is proposed based on the Lyapunov second method. By adjusting parameters, this new lemma can degenerate into previous ones and is, therefore, more general. Based on the proposed stability lemma and sliding mode technology, a new sliding mode surface is designed and an effective new sliding mode controller is designed to ensure that the system achieves synchronization within the predefined time. Moreover, the new effective sliding mode controller proposed in this paper has two advantages as follows: (1) The proposed sliding mode controller is robust against disturbances, which aligns more with practical application requirements. (2) The predefined time is set as the sliding mode controller parameter, avoiding overestimation of synchronization time. Finally, numerical simulations are presented to demonstrate the effectiveness of the proposed approach.