Synchronization for Nonlinear Complex Spatio-Temporal Networks with Multiple Time-Invariant Delays and Multiple Time-Varying Delays

  • Chengdong YangEmail author
  • Tingwen Huang
  • Kejia Yi
  • Ancai Zhang
  • Xiangyong Chen
  • Zhenxing Li
  • Jianlong Qiu
  • Fuad E. Alsaadi


This paper deals with the problem for synchronization of a nonlinear time delayed complex spatio-temporal network (CSN), modelled by semi-linear parabolic partial differential-difference equations. A boundary controller relying to distributed measurement is designed. Multiple time-invariant delays are firstly considered. By employing Lyapunov’s direct method and Wirtingers inequality, synchronization criteria of the CSN are presented in terms of LMIs. And then, multiple time-varying delays are respectively considered using the boundary controller and synchronization criteria are obtained. Finally, an example illustrates the effectiveness of the proposed method.


Complex networks Synchronization Boundary control Linear matrix inequalities 



The authors would like to thank the editor and anonymous reviewers for their valuable comments and suggestions. This work was jointly supported by the National Natural Science Foundation of China (Grant Nos. 61703193, 61773193 and 61503171), the Natural Science Foundation of Shandong Province (Grant Nos. ZR2017MF022, ZR2016JL021 and ZR2015FL021), the Key Research and Development Project of Shandong Province (Grant No. 2016GGX109001), the Key Research and Development Project of Linyi City (Grant No. 2017GGH009), the Funding of Young Teacher Growth Plan of Shandong Province, and the National Priority Research Project from the Qatar National Research Fund (Grant No. 9-166-1-031).


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Information Science and TechnologyLinyi UniversityLinyiPeople’s Republic of China
  2. 2.Key Laboratory of Complex Systems and Intelligent Computing in Universities of Shandong (Linyi University)LinyiPeople’s Republic of China
  3. 3.Texas A&M University at QatarDohaQatar
  4. 4.Technology Development DepartmentSystems Engineering Research Institute of CSSCBeijingChina
  5. 5.School of Automation and Electrical EngineeringLinyi UniversityLinyiPeople’s Republic of China
  6. 6.Department of Electrical and Computer Engineering, Faculty of EngineeringKing Abdulaziz UniversityJeddahSaudi Arabia

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