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Novel robust stability criteria for uncertain parameter quaternionic neural networks with mixed delays: Whole quaternionic method

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  • Pan, Jie
  • Pan, Zhaoya

Abstract

This paper concentrates on the robust stability of uncertain parameter quaternionic neural networks (QNNs) with both time-varying delays and infinite distributed delays. To this end, a derivative formula of quaternionic function’s norm is firstly established. Then, based on this formula, algebraic standards are obtained by employing M-matrix theory as well as analytical techniques to guarantee the global robust exponential stability of the considered QNNs. Particularly, different from most existing decomposition approaches, this whole quaternionic method can be used whether the QNNs are decomposable or not and greatly reduces computation cost. The utility of the easy-to-use results formulated in the form of quaternionic norm’s M-matrix is confirmed by three given instances with numerical simulation.

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  • 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).
    • Handle: RePEc:eee:apmaco:v:407:y:2021:i:c:s009630032100415x
    DOI: 10.1016/j.amc.2021.126326
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    References listed on IDEAS

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    1. 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).
    2. Tu, Zhengwen & Zhao, Yongxiang & Ding, Nan & Feng, Yuming & Zhang, Wei, 2019. "Stability analysis of quaternion-valued neural networks with both discrete and distributed delays," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 342-353.
    3. Liu, Shuxin & Yu, Yongguang & Zhang, Shuo & Zhang, Yuting, 2018. "Robust stability of fractional-order memristor-based Hopfield neural networks with parameter disturbances," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 845-854.
    4. Liu, Jin & Jian, Jigui & Wang, Baoxian, 2020. "Stability analysis for BAM quaternion-valued inertial neural networks with time delay via nonlinear measure approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 174(C), pages 134-152.
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    1. Deng, Jie & Li, Hong-Li & Cao, Jinde & Hu, Cheng & Jiang, Haijun, 2023. "State estimation for discrete-time fractional-order neural networks with time-varying delays and uncertainties," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).

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