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Quasi-Stabilization Control of Quaternion-Valued Fractional-Order Memristive Neural Networks

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Abstract

This paper focuses on the quasi-stabilization of the quaternion-valued fractional-order memristive neural networks. Based on the contraction mapping theory, a sufficient condition is derived to ensure the existence of the equilibrium point for the memristive neural networks. Subsequently, by means of Lyapunov functional and fractional Laplace transform, a algebraic inequality-based condition is developed to guarantee the quasi-stability of the equilibrium point. In addition, a related question is whether the convex closure proposed by the quaternion parameters is meaningful, to overcome this issues, a vector ordering approach is proposed, which can be used to compare the “magnitude” of two different quaternions. Finally, the corresponding simulation results are included to show the effectiveness of the proposed methodology derived in this paper.

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All data generated or analyzed during this study are included in this published article.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Shaanxi Normal University, Xi’an, 710062, China

    Ruoxia Li

  2. School of Mathematics, Southeast University, Nanjing, 210096, China

    Jinde Cao

  3. Yonsei Frontier Lab, Yonsei University, Seoul, 03722, South Korea

    Jinde Cao

Authors
  1. Ruoxia Li
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  2. Jinde Cao
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Correspondence to Ruoxia Li.

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This work was supported by the Young Talent Fund of Association for Science and Technology in Xi’an, China under grant No. 095920221333, and the Fundamental Research Funds for the Central Universities under grant No. GK202103005.

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Li, R., Cao, J. Quasi-Stabilization Control of Quaternion-Valued Fractional-Order Memristive Neural Networks. Circuits Syst Signal Process 41, 6733–6749 (2022). https://doi.org/10.1007/s00034-022-02105-4

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  • DOI: https://doi.org/10.1007/s00034-022-02105-4

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