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Global stability of Clifford-valued recurrent neural networks with time delays

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Abstract

In this paper, we study an issue of stability analysis for Clifford-valued recurrent neural networks (RNNs) with time delays. As an extension of real-valued neural network, the Clifford-valued neural network, which includes familiar complex-valued neural network and quaternion-valued neural network as special cases, has been an active research field recently. To the best of our knowledge, the stability problem for Clifford-valued systems with time delays has still not been solved. We first explore the existence and uniqueness for the equilibrium of delayed Clifford-valued RNNs, based on which some sufficient conditions ensuring the global asymptotic and exponential stability of such systems are obtained in terms of a linear matrix inequality (LMI). The simulation result of a numerical example is also provided to substantiate the effectiveness of the proposed results.

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Acknowledgments

The authors wish to thank the editor and reviewers for a number of constructive comments and suggestions that have improved the quality of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China

    Yang Liu & Pei Xu

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

    Yang Liu, Jianquan Lu & Jinling Liang

Authors
  1. Yang Liu
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  2. Pei Xu
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  3. Jianquan Lu
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  4. Jinling Liang
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Corresponding author

Correspondence to Yang Liu.

Additional information

This work was partially supported by Zhejiang Provincial Natural Science Foundation of China under Grant no. LY14A010008, the National Natural Science Foundation of China under Grant Nos. 61573102, 61374077, 61174136, and 61175119, and the China Postdoctoral Science Foundation under Grant No. 2015M580378.

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Liu, Y., Xu, P., Lu, J. et al. Global stability of Clifford-valued recurrent neural networks with time delays. Nonlinear Dyn 84, 767–777 (2016). https://doi.org/10.1007/s11071-015-2526-y

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