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An Improved Fixed-Time Stability Theorem and its Application to the Synchronization of Stochastic Impulsive Neural Networks

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Abstract

In this paper, the fixed-time synchronization of stochastic impulsive neural networks with time-varying delays is studied. For the stability problem of nonlinear systems with impulsive effects, a new fixed-time stability theorem is proposed. Compared with other fixed-time stability theorems, it has better generality. Then, in order to realize fixed-time synchronization, a state feedback controller and an adaptive controller are designed respectively. Moreover, based on the new theorem, sufficient conditions for fixed-time synchronization of stochastic impulsive neural networks with time-varying delays are given. Finally, two simulation examples are given to verify the effectiveness of the theoretical results.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Nos. 62103165, 62101213 and 12026211), Shandong Provincial Natural Science Foundation (No. ZR2022ZD01), Shandong Provincial Higher Educational Youth Innovation Science and Technology Program (No. 2019KJN029), and Development Program Project of Youth Innovation Team of Institutions of Higher Learning in Shandong Province.

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Authors and Affiliations

  1. Shandong Provincial Key Laboratory of Network Based Intelligent Computing, School of Information Science and Engineering, University of Jinan, Jinan, 250022, China

    Qingjie Wang, Hui Zhao, Aidi Liu, Sijie Niu, Xizhan Gao & Xiju Zong

  2. Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Lixiang Li

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  1. Qingjie Wang
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  2. Hui Zhao
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  5. Xizhan Gao
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  7. Lixiang Li
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Correspondence to Hui Zhao.

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Wang, Q., Zhao, H., Liu, A. et al. An Improved Fixed-Time Stability Theorem and its Application to the Synchronization of Stochastic Impulsive Neural Networks. Neural Process Lett 55, 7447–7467 (2023). https://doi.org/10.1007/s11063-023-11268-3

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