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A LMI-based approach to global asymptotic stability of neural networks with time varying delays

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Abstract

In this paper, the asymptotic stability of neural networks with time varying delay is studied by using the nonsmooth analysis, Lyapunov functional method and linear matrix inequality (LMI) technique. It is noted that the proposed results do not require smoothness of the behaved function and activation function as well as boundedness of the activation function. Several sufficient conditions are presented to show the uniqueness and the global asymptotical stability of the equilibrium point. Also, a high-dimensional matrix condition to ensure the uniqueness and the global asymptotical stability of equilibrium point can be reduced to a low-dimensional condition. The obtained results are easy to apply and improve some earlier works. Finally, we give two simulations to justify the theoretical analysis in this paper.

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Authors and Affiliations

  1. Department of Mathematics, Southeast University, Nanjing, 210096, China

    Wenwu Yu

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  1. Wenwu Yu
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Correspondence to Wenwu Yu.

Additional information

This work was supported by the Natural Science Foundation of Jiangsu Province of China under Grant No. BK2006093.

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Yu, W. A LMI-based approach to global asymptotic stability of neural networks with time varying delays. Nonlinear Dyn 48, 165–174 (2007). https://doi.org/10.1007/s11071-006-9080-6

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  • DOI: https://doi.org/10.1007/s11071-006-9080-6

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