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Stochastic stabilization of Markov jump quaternion-valued neural network using sampled-data control

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  • Shu, Jinlong
  • Wu, Baowei
  • Xiong, Lianglin
  • Wu, Tao
  • Zhang, Haiyang

Abstract

This paper investigates the stochastic stabilization of Markov jump quaternion-valued neural networks (QVNNs) using a sampled-data control strategy. Firstly, Markov jump QVNNs are decomposed into two complex-valued systems using the plural decomposition method because the multiplication of quaternions is not commutative. Secondly, the existence and uniqueness of the equilibrium point of the Markov jump QVNNs is proved according to the theory of homeomorphism mapping. Thirdly, by choosing a suitable Lyapunov-Krasovskii functional and combining some inequality techniques, a new stochastic stability criterion is established for the Markov jump QVNNs. Based on this, several verifiable sufficient conditions for the stochastic stabilization of Markov jump QVNNs with sampled-data control are ensured. Finally, the correctness and effectiveness of the proposed method are verified by two numerical examples.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:400:y:2021:i:c:s0096300321000898
    DOI: 10.1016/j.amc.2021.126041
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    References listed on IDEAS

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    1. Ting Lei & Qiankun Song & Zhenjiang Zhao & Jianxi Yang, 2013. "Synchronization of Chaotic Neural Networks with Leakage Delay and Mixed Time-Varying Delays via Sampled-Data Control," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, November.
    2. 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).
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    Cited by:

    1. Nguyen, Khanh Hieu & Kim, Sung Hyun, 2022. "Improved sampled-data control design of T-S fuzzy systems against mismatched fuzzy-basis functions," Applied Mathematics and Computation, Elsevier, vol. 428(C).
    2. Xu, Qiyi & Zhang, Ning & Qi, Wenhai, 2023. "Finite-time control for discrete-time nonlinear Markov switching LPV systems with DoS attacks," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    3. Zhang, Jianan & Ma, Yuechao, 2023. "Adaptive fault-tolerant double asynchronous control for switched semi-Markov jump systems via improved memory sampled-data technique," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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