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Global synchronization of multi-weighted complex dynamical networks with multiple time-varying delays via PI/PD control

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Abstract

In this paper, the multiple weighted complex dynamical networks (MWCDNs) with multiple time-varying delays (MTDs) is introduced. The main purpose of this paper is to study the global synchronization of MWCDNs with MTDs by designing novel PI/PD controllers which is related to the number of subsystems in networks. Firstly, in order to study the global synchronization problem of MWCDNs with MTDs based on the novel PI controller, a new type of Lyapunov-Krasovskii function is established in this paper which contains the integral term of PI controller. Secondly, by using Jensen’s inequality and Newton-Leibniz formulas, sufficient conditions for the global synchronization of MWCDNs with MTDs based on PI/PD controllers are obtained in the form of linear matrix inequalities. Finally, two numerical examples are used to illustrate the advantages and validity of the theoretical results we obtained.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China No. 61273004, and the Natural Science Foundation of Hebei province No. F2021203061. The authors also gratefully acknowledge the helpful comments and suggestions of the reviewers, which have improved the presentation.

Funding

This work is supported by National Natural Science Foundation of China (No. 61273004) and the Natural Science Foundation of Hebei province (No. F2021203061).

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Authors and Affiliations

  1. School of Science, Yanshan University, Qinhuangdao, Hebei, 066004, People’s Republic of China

    Wenying Yuan, Shengli Shi & Yuechao Ma

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  1. Wenying Yuan
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  2. Shengli Shi
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  3. Yuechao Ma
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Correspondence to Yuechao Ma.

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Yuan, W., Shi, S. & Ma, Y. Global synchronization of multi-weighted complex dynamical networks with multiple time-varying delays via PI/PD control. Neural Comput & Applic 34, 4047–4068 (2022). https://doi.org/10.1007/s00521-021-06663-7

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  • DOI: https://doi.org/10.1007/s00521-021-06663-7

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