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Global stability and stabilization for inertial memristive neural networks with unbounded distributed delays

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Abstract

This paper investigates the stability and stabilization of inertial memristive neural networks (IMNNs) with discrete and unbounded distributed delays. The considered IMNNs are described as hybrid neural systems with second-order derivatives due to the combination of memristor and inertial items. By invoking an appropriate variable substitution method, the hybrid neural system is turned into a first-order differential system. Then, based on the nonsmooth analysis and Lyapunov stability theories, several new algebraic conditions for the global stability of IMNNs with unbounded distributed delays are derived. In addition, two simple classes of feedback control laws are designed for the considered IMNNs and the corresponding stabilizability criteria are established. Finally, two numerical examples and their discussions are provided to illustrate the validity and superiority of the theoretical results.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grants 61703377, 61703374, 61876192, and 61603419, and the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) under Grants CUG170632 and CUG170656.

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Authors and Affiliations

  1. School of Automation, China University of Geosciences, Wuhan, 430074, China

    Leimin Wang

  2. Hubei key Laboratory of Advanced Control and Intelligent Automation for Complex Systems, Wuhan, China

    Leimin Wang

  3. School of Mechanical Engineering and Electronic Information, China University of Geosciences, Wuhan, 430074, China

    Ming-Feng Ge

  4. College of Mathematics and Statistics, South-Central University for Nationalities, Wuhan, 430074, China

    Junhao Hu & Guodong Zhang

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  1. Leimin Wang
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  2. Ming-Feng Ge
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Correspondence to Leimin Wang.

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Wang, L., Ge, MF., Hu, J. et al. Global stability and stabilization for inertial memristive neural networks with unbounded distributed delays. Nonlinear Dyn 95, 943–955 (2019). https://doi.org/10.1007/s11071-018-4606-2

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