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Effect of Impulses on Robust Exponential Stability of Delayed Quaternion-Valued Neural Networks

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Abstract

This paper investigates the dynamic behavior of a class of delayed quaternion-valued neural networks (QVNNs) with impulses and parameter uncertainties. First, we assume that the activation function and connection matrices in the model are defined in the quaternion domain. Without decomposing the QVNNs into four equivalent neural networks in a real number domain or two equivalent neural networks in a complex number domain, the existence and uniqueness of the equilibrium point (EP) are studied based on the M-matrix and homeomorphism mapping theories. By combing the vector Lyapunov function with mathematical induction, theorems are given to ensure robust exponential stability of the system’s EP. The results reflect the influence of connection matrices, delays, impulses, and the activation function on the convergence speed of the EP. Finally, the feasibility of the derived results is explained through three examples.

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Acknowledgements

This work is supported in part by the Key Research and Development Project of Sichuan Province under Grant Nos. 2023YFG0067, 2022YFG0094 and 2021YFG0071, in part by the Regional Cooperation and Innovation Project of Sichuan Province under Grant No. 2021YFQ0052, and in part by the Open Project Funding of Engineering Research Center of Advanced Energy Saving Driving Technology, Ministry of Education.

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Authors and Affiliations

  1. Vehicle Measurement, Control and Safety Key Laboratory of Sichuan Province, Xihua University, Chengdu, 610039, People’s Republic of China

    Xiaohui Xu, Haolin Yang & Shulei Sun

  2. Provincial Engineering Research Center for New Energy Vehicle Intelligent Control and Simulation Test Technology of Sichuan, Xihua University, Chengdu, 610039, People’s Republic of China

    Xiaohui Xu & Jibin Yang

  3. Engineering Research Center of Advanced Energy Saving Driving Technology, Ministry of Education, Chengdu, 610031, People’s Republic of China

    Shulei Sun

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  1. Xiaohui Xu
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Contributions

Xiaohui Xu and Jibin Yang wrote the main manuscript text. Haolin Yang prepared Figs. 5, 6, 7, 8 and 9. Shulei Sun prepared Figs. 1, 2, 3 and 4. All authors have reviewed the manuscript.

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Correspondence to Jibin Yang.

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Xu, X., Yang, J., Yang, H. et al. Effect of Impulses on Robust Exponential Stability of Delayed Quaternion-Valued Neural Networks. Neural Process Lett 55, 9615–9634 (2023). https://doi.org/10.1007/s11063-023-11217-0

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