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Stability and synchronization control of inertial neural networks with mixed delays

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  • Li, Wenhua
  • Gao, Xingbao
  • Li, Ruoxia

Abstract

This paper analyzes the stability and synchronization control of inertial neural networks (INNs) with both time-varying delay and coupling delay by transforming them into the first-order systems. We show that there exists a unique equilibrium point (EP) by generalized nonlinear measure (GNM) approach, and provide a criterion to ensure the global asymptotic stability (GAS) of the EP by defining an appropriate Lyapunov–Krasovskii functional (LKF). Moreover, for the addressed systems under parameter mismatch, the quasi-synchronization is realized by applying the generalized Halanary inequality and matrix measure (MM), and an adaptive controller is designed to achieve the global asymptotic synchronization. The obtained results improve some exiting ones and are easy to be checked. Finally, the validity of the obtained results is supported by some numerical examples.

Suggested Citation

  • Li, Wenhua & Gao, Xingbao & Li, Ruoxia, 2020. "Stability and synchronization control of inertial neural networks with mixed delays," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    • Handle: RePEc:eee:apmaco:v:367:y:2020:i:c:s0096300319307714
    DOI: 10.1016/j.amc.2019.124779
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    References listed on IDEAS

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    1. Chen, Chuan & Li, Lixiang & Peng, Haipeng & Yang, Yixian & Mi, Ling & Qiu, Baolin, 2019. "Fixed-time projective synchronization of memristive neural networks with discrete delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    2. 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.
    3. Wang, Jing & Hu, Xiaohui & Wei, Yunliang & Wang, Zhen, 2019. "Sampled-data synchronization of semi-Markov jump complex dynamical networks subject to generalized dissipativity property," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 853-864.
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    Cited by:

    1. 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).
    2. Jia, Jinping & Dai, Hao & Li, Li & Zhang, Fandi, 2021. "Global sampled-data stabilization for a class of nonlinear systems with arbitrarily long input delays via a multi-rate control algorithm," Applied Mathematics and Computation, Elsevier, vol. 392(C).

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