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Passivity analysis of delayed neural networks with discontinuous activations via differential inclusions

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Abstract

Without assuming the boundedness and monotonicity of neuron activations, we investigate passivity of delayed neural networks with discontinuous activations. Based on differential inclusion theory, sufficient conditions are established in form of linear matrix inequality by employing the generalized Lyapunov approach. In addition, a kind of control input is designed to stabilize neural network with activation functions having special form. Finally, some numerical examples are proposed to show the effectiveness of developed results.

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Acknowledgements

The work is supported by the Natural Science Foundation of China under Grants 60974021 and 61125303, the 973 Program of China under Grant 2011CB710606 and the Fund for Distinguished Young Scholars of Hubei Province under Grant 2010CDA081.

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Authors and Affiliations

  1. Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China

    Jian Xiao, Zhigang Zeng, Wenwen Shen & Ailong Wu

  2. Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Wuhan, 430074, China

    Jian Xiao, Zhigang Zeng, Wenwen Shen & Ailong Wu

  3. College of Mathematics and Statistics, Hubei Normal University, Huangshi, 435002, China

    Ailong Wu

Authors
  1. Jian Xiao
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  2. Zhigang Zeng
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  3. Wenwen Shen
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  4. Ailong Wu
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Correspondence to Jian Xiao.

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Xiao, J., Zeng, Z., Shen, W. et al. Passivity analysis of delayed neural networks with discontinuous activations via differential inclusions. Nonlinear Dyn 74, 213–225 (2013). https://doi.org/10.1007/s11071-013-0959-8

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  • DOI: https://doi.org/10.1007/s11071-013-0959-8

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