Delayed Pinning Control for Synchronization of Dynamical Networks

• 成果类型: Article
• 署名作者: Zhu, Shuaibing; Li, Feng; Deng, Zhenhua; Lu, Jinhu
• 署名单位: Hunan Normal University; Anhui University of Technology; Central South University; Beihang University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3568558
• 发表日期: 2025
• 页码: 7008-7015
• 关键词: Delays; Synchronization; trajectory; vectors; Symmetric matrices; Delay effects; Couplings; PROCESS CONTROL; Upper bound; training; Delayed pinning control (DPC); dynamical networks; lag synchronization (LS); quasi-synchronization

摘要

Although pinning control of dynamical networks with or without delay has been well explored in the past two decades, little attention has been paid to the delay originated from pinning control itself. This article investigates the delayed pinning control scheme for lag synchronization and lag quasi-synchronization of dynamical networks. Two pinning control schemes with uniform delay and nonuniform delays are proposed, which are more practical than the widely used delay-free pinning control scheme. For the two pinning control schemes, criteria for lag synchronization and lag quasi-synchronization of dynamical networks are derived by proposing a system of functional differential inequalities, and in the meantime, an upper bound of tolerable delays that allows synchronization is given. In particular, the ultimate bound of the synchronization error is estimated for lag quasi-synchronization. Finally, the theoretical results are demonstrated by two numerical examples.