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Reachable set estimation of delayed Markovian jump neural networks via variables-augmented-based free-weighting-matrices method

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  • Chang, Xu-Kang
  • He, Yong

Abstract

The problem of the reachable set estimation for delayed Markovian jump neural networks is investigated in this article. Firstly, to take full account of the information of state variables and time delay, an augmented delay-product-type Lyapunov-Krasovskii functional (LKF) is established for obtaining an accurate reachable set described by an ellipsoid. Some single and quadratic integral states are introduced into the LKF as augmented variables to reduce the conservatism of the reachable set result. However, the introduction of the integral states causes the LKF derivative to generate higher-order terms of the time-varying delay. Then, the variables-augmented-based free-weighting-matrices method is introduced to solve this problem. The method makes the LKF derivative turn into a linear function and gives more freedom to derive an improved result. Finally, a more accurate reachable set is obtained, whose merits are shown by a numerical example.

Suggested Citation

  • Chang, Xu-Kang & He, Yong, 2024. "Reachable set estimation of delayed Markovian jump neural networks via variables-augmented-based free-weighting-matrices method," Applied Mathematics and Computation, Elsevier, vol. 478(C).
    • Handle: RePEc:eee:apmaco:v:478:y:2024:i:c:s0096300324002984
    DOI: 10.1016/j.amc.2024.128837
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    References listed on IDEAS

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    1. Shu, Jinlong & Wu, Baowei & Xiong, Lianglin, 2022. "Stochastic stability criteria and event-triggered control of delayed Markovian jump quaternion-valued neural networks," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    2. Lee, Tae H. & Park, Myeong Jin & Park, Ju H., 2021. "An improved stability criterion of neural networks with time-varying delays in the form of quadratic function using novel geometry-based conditions," Applied Mathematics and Computation, Elsevier, vol. 404(C).
    3. Yong He & Chuan-Ke Zhang & Hong-Bing Zeng & Min Wu, 2023. "Additional functions of variable-augmented-based free-weighting matrices and application to systems with time-varying delay," International Journal of Systems Science, Taylor & Francis Journals, vol. 54(5), pages 991-1003, April.
    4. Liu, Guobao & Chen, Xiangyong & Shen, Zhongyu & Liu, Yajuan & Jia, Xianglei, 2022. "Reachable set estimation for continuous delayed singularly perturbed systems with bounded disturbances," Applied Mathematics and Computation, Elsevier, vol. 416(C).
    5. Jiao, Shiyu & Shen, Hao & Wei, Yunliang & Huang, Xia & Wang, Zhen, 2018. "Further results on dissipativity and stability analysis of Markov jump generalized neural networks with time-varying interval delays," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 338-350.
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