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Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks

Author

Listed:
  • Grienggrai Rajchakit

    (Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai 50290, Thailand)

  • Pharunyou Chanthorn

    (Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

  • Pramet Kaewmesri

    (Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang mod, Thung Khru 10140, Thailand)

  • Ramalingam Sriraman

    (Vel Tech High Tech Dr.Rangarajan Dr.Sakunthala Engineering College, Avadi, Tamil Nadu-600 062, India)

  • Chee Peng Lim

    (Institute for Intelligent Systems Research and Innovation, Deakin University, Waurn Ponds, VIC 3216, Australia)

Abstract

This paper studies the global Mittag–Leffler stability and stabilization analysis of fractional-order quaternion-valued memristive neural networks (FOQVMNNs). The state feedback stabilizing control law is designed in order to stabilize the considered problem. Based on the non-commutativity of quaternion multiplication, the original fractional-order quaternion-valued systems is divided into four fractional-order real-valued systems. By using the method of Lyapunov fractional-order derivative, fractional-order differential inclusions, set-valued maps, several global Mittag–Leffler stability and stabilization conditions of considered FOQVMNNs are established. Two numerical examples are provided to illustrate the usefulness of our analytical results.

Suggested Citation

  • Grienggrai Rajchakit & Pharunyou Chanthorn & Pramet Kaewmesri & Ramalingam Sriraman & Chee Peng Lim, 2020. "Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks," Mathematics, MDPI, vol. 8(3), pages 1-29, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:422-:d:332701
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    References listed on IDEAS

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    Cited by:

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    3. Rajchakit, G. & Sriraman, R. & Lim, C.P. & Unyong, B., 2022. "Existence, uniqueness and global stability of Clifford-valued neutral-type neural networks with time delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 508-527.
    4. Zhang, Zhengqiu & Yang, Zhen, 2023. "Asymptotic stability for quaternion-valued fuzzy BAM neural networks via integral inequality approach," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    5. Usa Humphries & Grienggrai Rajchakit & Pramet Kaewmesri & Pharunyou Chanthorn & Ramalingam Sriraman & Rajendran Samidurai & Chee Peng Lim, 2020. "Global Stability Analysis of Fractional-Order Quaternion-Valued Bidirectional Associative Memory Neural Networks," Mathematics, MDPI, vol. 8(5), pages 1-27, May.
    6. Iswarya, M. & Raja, R. & Cao, J. & Niezabitowski, M. & Alzabut, J. & Maharajan, C., 2022. "New results on exponential input-to-state stability analysis of memristor based complex-valued inertial neural networks with proportional and distributed delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 440-461.
    7. Shen, Shiping & Meng, Xiaofang, 2023. "Finite-time stability of almost periodic solutions of Clifford-valued RNNs with time-varying delays and D operator on time scales," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    8. Gan, Binbin & Chen, Hao & Xu, Biao & Kang, Wei, 2023. "A norm stability condition of neutral-type Cohen-Grossberg neural networks with multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    9. Yang, Zhanying & Zhang, Jie & Zhang, Zhihui & Mei, Jun, 2023. "An improved criterion on finite-time stability for fractional-order fuzzy cellular neural networks involving leakage and discrete delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 910-925.
    10. Babu, N. Ramesh & Balasubramaniam, P., 2022. "Master-slave synchronization of a new fractal-fractional order quaternion-valued neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

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