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Robustness Analysis for Connection Weight Matrices of Global Exponential Stability of Stochastic Delayed Recurrent Neural Networks

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Abstract

In this paper, we analyze the robustness of global exponential stability of stochastic delayed recurrent neural networks (SDRNNs) subject to parameter uncertainties in connection weight matrices. Given a globally exponentially stable SDRNN, the problem to be addressed here is how much the parameter uncertainties in connection weight matrices the SDRNN can withstand to be globally exponentially stable. Different from the traditional Lyapuvon stability theory, we only use the coefficients of global exponential stability. The upper bounds of parameter uncertainties are characterized using transcendental equations for the SDRNNs to sustain globally exponentially stable. Moreover, we prove theoretically that, for any globally exponentially stable SDRNNs, if additive parameter uncertainties in connection weight matrices are smaller than the derived upper bounds at here, then the perturbed SDRNNs are guaranteed to also be globally exponentially stable. A numerical example is provided here to illustrate the theoretical results.

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Acknowledgments

The authors would like to thank the associate editor and the referees for their detailed comments and valuable suggestions, which considerably improved the presentation of this paper. This work was supported by the Key Program of National Natural Science Foundation of China with Grant No. 61134012, National Natural Science Foundation of China with Grant No. 61203055, 11271146 and supported by the Fundamental Research Funds for the Central Universities of 2013XK03.

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Authors and Affiliations

  1. College of Science, China University of Mining and Technology, Xuzhou , 221116, Jiangsu, People’s Republic of China

    Song Zhu & Weiwei Luo

  2. College of Automation, Huazhong University of Science and Technology, Wuhan,  430074, Hubei, People’s Republic of China

    Yi Shen

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  1. Song Zhu
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  2. Weiwei Luo
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  3. Yi Shen
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Correspondence to Song Zhu.

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Zhu, S., Luo, W. & Shen, Y. Robustness Analysis for Connection Weight Matrices of Global Exponential Stability of Stochastic Delayed Recurrent Neural Networks. Circuits Syst Signal Process 33, 2065–2083 (2014). https://doi.org/10.1007/s00034-013-9735-8

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  • DOI: https://doi.org/10.1007/s00034-013-9735-8

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