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Global polynomial synchronization for quaternion-valued T–S fuzzy inertial neural networks via event-triggered control: A polynomial gain method

Author

Listed:
  • Zhang, Jingjing
  • Li, Zhouhong
  • Cao, Jinde
  • Abdel-Aty, Mahmoud
  • Meng, Xiaofang

Abstract

This work explores the global polynomial synchronization for a class of quaternion-valued Takagi–Sugeno fuzzy inertial neural networks based on event-triggered control. Firstly, the paper designs the fuzzy event-triggered controller with a polynomial gain, a unique approach to optimize the event-triggered mechanism. The non-reduced order and non-decomposition methods are applied to maintain computational efficiency without introducing new variables. Then, under static and dynamic event-triggered conditions, the system’s global polynomial synchronization is guaranteed by formulating a suitable delay-free Lyapunov functional and using quaternion properties and inequality techniques. Moreover, rigorous derivation is employed to verify a positive lower bound of any event-triggered interval, concluding that the system does not produce Zeno behavior. Finally, a numerical example and the application of image encryption and decryption are presented to strongly validate the reliability of the model and control mechanism in achieving global polynomial synchronization.

Suggested Citation

  • Zhang, Jingjing & Li, Zhouhong & Cao, Jinde & Abdel-Aty, Mahmoud & Meng, Xiaofang, 2025. "Global polynomial synchronization for quaternion-valued T–S fuzzy inertial neural networks via event-triggered control: A polynomial gain method," Chaos, Solitons & Fractals, Elsevier, vol. 196(C).
    • Handle: RePEc:eee:chsofr:v:196:y:2025:i:c:s0960077925004163
    DOI: 10.1016/j.chaos.2025.116403
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    References listed on IDEAS

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    1. Luo, Lingao & Li, Lulu & Huang, Wei, 2024. "Asymptotic stability of fractional-order Hopfield neural networks with event-triggered delayed impulses and switching effects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 491-504.
    2. Xiong, Kailong & Hu, Cheng & Yu, Juan, 2023. "Direct approach-based synchronization of fully quaternion-valued neural networks with inertial term and time-varying delay," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
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