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New fixed-time stability criterion and fixed-time synchronization of neural networks via non-chattering control

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Abstract

Based on the framework of Filippov solution, a non-chattering controller is presented to realize the fixed-time (FXT) stability for a nonlinear system with the discontinuous activation function. First, a novel FXT stability criterion is established through the reduction to absurdity, and the settling time is estimated. Then, by building two controllers without chattering, sufficient conditions are obtained to ensure the FXT synchronization of the drive-response system. Moreover, compared with the existing results, the FXT obtained here is less conservative and more accurate. Finally, the validity of the proposed methods is provided by two numerical examples.

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Acknowledgements

The authors are grateful for the support of the National Natural Science Foundation of China (Grant No. 61673190); the Fundamental Research Funds for the Central Universities under Grant CCNU22JC011; the Natural Science Foundation Project of Chongqing No. cstc2021jcyj-msxmX0051; the Science and Technology Innovation Project of Economic Circle Construction in Chengdu-Chongqing Area under Grant No. KJCX2020047 and the Graduate Innovation Program of CCNU (2022CXZZ103).

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Authors and Affiliations

  1. College of Physical Science and Technology, Central China Normal University, Wuhan, 430079, China

    Qian Tang, Shaocheng Qu, Wei Zheng & Xiaona Du

  2. College of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing, 404100, China

    Zhengwen Tu

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  1. Qian Tang
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Correspondence to Shaocheng Qu.

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Tang, Q., Qu, S., Zheng, W. et al. New fixed-time stability criterion and fixed-time synchronization of neural networks via non-chattering control. Neural Comput & Applic 35, 6029–6041 (2023). https://doi.org/10.1007/s00521-022-07975-y

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