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

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Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. School of Information Science and Technology, Linyi University, Linyi, 276005, People’s Republic of China

    Chengdong Yang

  2. Key Laboratory of Complex Systems and Intelligent Computing in Universities of Shandong (Linyi University), Linyi, 276005, People’s Republic of China

    Chengdong Yang, Ancai Zhang, Xiangyong Chen, Zhenxing Li & Jianlong Qiu

  3. Texas A&M University at Qatar, Doha, 5825, Qatar

    Tingwen Huang

  4. Technology Development Department, Systems Engineering Research Institute of CSSC, Beijing, 100039, China

    Kejia Yi

  5. School of Automation and Electrical Engineering, Linyi University, Linyi, 276005, People’s Republic of China

    Ancai Zhang, Xiangyong Chen, Zhenxing Li & Jianlong Qiu

  6. Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    Jianlong Qiu & Fuad E. Alsaadi

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  1. Chengdong Yang
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  2. Tingwen Huang
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  3. Kejia Yi
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  4. Ancai Zhang
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  8. Fuad E. Alsaadi
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Correspondence to Chengdong Yang.

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Yang, C., Huang, T., Yi, K. et al. Synchronization for Nonlinear Complex Spatio-Temporal Networks with Multiple Time-Invariant Delays and Multiple Time-Varying Delays. Neural Process Lett 50, 1051–1064 (2019). https://doi.org/10.1007/s11063-018-9900-y

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