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Finite-Time Stability and Its Application for Solving Time-Varying Sylvester Equation by Recurrent Neural Network

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Abstract

This paper investigates finite-time stability and its application for solving time-varying Sylvester equation by recurrent neural network. Firstly, a new finite-time stability criterion is given and a less conservative upper bound of the convergence time is also derived. Secondly, a sign-bi-power activation function with a linear term is presented for the recurrent neural network. The estimation of the upper bound of the convergence time is more less conservative. Thirdly, it is proposed a tunable activation function with three tunable positive parameters for the recurrent neural network. These parameters are not only helpful to reduce conservatism of the upper bound of the convergence time, accelerate convergence but also reduce sensitivity to additive noise. The effectiveness of our methods is shown by both theoretical analysis and numerical simulations.

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Acknowledgments

This work was supported by the National Science Foundation of China (No. 61374028, 61273183, 51177088), the Grant National Science Foundation of Hubei Provincial (2013CFA05 0), the Graduate Scientific Research Foundation of China Three Gorges University (2014PY069).

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Authors and Affiliations

  1. College of Electrical Engineering and New Energy, China Three Gorges University, Yichang, 443002, Hubei, China

    Yanjun Shen & Yuehua Huang

  2. College of Science, China Three Gorges University, Yichang, 443002, Hubei, China

    Peng Miao

  3. Department of Basic Courses, Zhengzhou Science and Technology University, Zhengzhou, 450064, Hennan, China

    Peng Miao

  4. College of Automation, Huazhong University of Science and Technology, Wuhan, 430074, Hubei, China

    Yi Shen

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  1. Yanjun Shen
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  2. Peng Miao
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  3. Yuehua Huang
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  4. Yi Shen
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Correspondence to Yanjun Shen.

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Shen, Y., Miao, P., Huang, Y. et al. Finite-Time Stability and Its Application for Solving Time-Varying Sylvester Equation by Recurrent Neural Network. Neural Process Lett 42, 763–784 (2015). https://doi.org/10.1007/s11063-014-9397-y

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