Science China Technological Sciences

, Volume 62, Issue 8, pp 1412–1422 | Cite as

On PID control for synchronization of complex dynamical network with delayed nodes

  • HaiBo Gu
  • JinHu LüEmail author
  • ZongLi Lin


Over the past two decades, synchronization, as an interesting collective behavior of complex dynamical networks, has been attracting much attention. To reveal and analyze the inherent mechanism of synchronization in complex dynamical networks with time delays in nodes, this paper attempts to use PD and PI control protocols to achieve synchronization. Based on a classical network model, we investigate the PD and PI control for synchronization of complex dynamical networks with delayed nodes and obtain some sufficient conditions. By using Lyapunov functions and appropriate state transformations, we prove that global synchronization can be achieved via the above control protocols. Finally, some simulation examples are illustrated to validate the effectiveness of the proposed theoretical results.


synchronization PID control complex dynamical network networked control system delayed node 


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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Key Laboratory of Systems and Control, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina
  2. 2.School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijingChina
  3. 3.School of Automation Science and Electrical Engineering, State Key Laboratory of Software Development Environment, and Beijing Advanced Innovation Center for Big Data and Brain Machine IntelligenceBeihang UniversityBeijingChina
  4. 4.Charles L. Brown Department of Electrical and Computer EngineeringUniversity of VirginiaCharlottesvilleUSA

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