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Stability and stabilization of quaternion-valued neural networks with uncertain time-delayed impulses: Direct quaternion method

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  • Tu, Zhengwen
  • Yang, Xinsong
  • Wang, Liangwei
  • Ding, Nan

Abstract

In this paper, the exponential stability of impulsive quaternion-valued neural networks (IQVNNs) with time delays is investigated. Both the differential equation and impulses are affected by time-varying delays which may be nonidentical. Uncertain parameters in impulses are also considered. Firstly, the existence and uniqueness of the equilibrium of the IQVNNs are discussed with the help of homeomorphic mapping theorem. Then, by utilizing Lyapunov functions and a newly developed inequality, several sufficient criteria are established in the form of quaternion-valued linear matrix inequalities (LMIs). It should be noted that, compared to most of existing results which are obtained by decomposing quaternion-valued neural networks (QVNNs) into four real-valued neural networks (RVNNs) or two complex-valued neural networks (CVNNs), our results are easier to be verified since the quaternion-valued LMIs exhibit lower dimensions. Then, based on obtained results, one impulsive controller is designed to realize the stabilization of delayed QVNNs. Finally, two numerical examples are presented to verify the effectiveness and merits of the theoretical analysis.

Suggested Citation

  • Tu, Zhengwen & Yang, Xinsong & Wang, Liangwei & Ding, Nan, 2019. "Stability and stabilization of quaternion-valued neural networks with uncertain time-delayed impulses: Direct quaternion method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    • Handle: RePEc:eee:phsmap:v:535:y:2019:i:c:s0378437119313585
    DOI: 10.1016/j.physa.2019.122358
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    Cited by:

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    3. Shu, Jinlong & Wu, Baowei & Xiong, Lianglin & Wu, Tao & Zhang, Haiyang, 2021. "Stochastic stabilization of Markov jump quaternion-valued neural network using sampled-data control," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    4. 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.
    5. Ju, Yanhao & Sun, Yuangong & Meng, Fanwei, 2020. "Stabilization of switched positive system with impulse and marginally stable subsystems: A mode-dependent dwell time method," Applied Mathematics and Computation, Elsevier, vol. 383(C).
    6. Li, Ruoxia & Cao, Jinde & Xue, Changfeng & Manivannan, R., 2021. "Quasi-stability and quasi-synchronization control of quaternion-valued fractional-order discrete-time memristive neural networks," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    7. Zhao, Rui & Wang, Baoxian & Jian, Jigui, 2022. "Global μ-stabilization of quaternion-valued inertial BAM neural networks with time-varying delays via time-delayed impulsive control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 223-245.
    8. Wang, Huamin & Wei, Guoliang & Wen, Shiping & Huang, Tingwen, 2021. "Impulsive disturbance on stability analysis of delayed quaternion-valued neural networks," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    9. Pan, Jie & Pan, Zhaoya, 2021. "Novel robust stability criteria for uncertain parameter quaternionic neural networks with mixed delays: Whole quaternionic method," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    10. Usa Humphries & Grienggrai Rajchakit & Pramet Kaewmesri & Pharunyou Chanthorn & Ramalingam Sriraman & Rajendran Samidurai & Chee Peng Lim, 2020. "Stochastic Memristive Quaternion-Valued Neural Networks with Time Delays: An Analysis on Mean Square Exponential Input-to-State Stability," Mathematics, MDPI, vol. 8(5), pages 1-26, May.

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