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Impulsive control of unstable neural networks with unbounded time-varying delays

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Abstract

This paper considers the impulsive control of unstable neural networks with unbounded time-varying delays, where the time delays to be addressed include the unbounded discrete time-varying delay and unbounded distributed time-varying delay. By employing impulsive control theory and some analysis techniques, several sufficient conditions ensuring μ-stability, including uniform stability, (global) asymptotical stability, and (global) exponential stability, are derived. It is shown that an unstable delay neural network, especially for the case of unbounded time-varying delays, can be stabilized and has μ-stability via proper impulsive control strategies. Three numerical examples and their simulations are presented to demonstrate the effectiveness of the control strategy.

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Acknowledgements

This work was jointly supported by National Natural Science Foundation of China (Grant Nos. 11301308, 61673247, 61273233), Outstanding Youth Foundation of Shandong Province (Grant Nos. ZR20170-2100145, ZR2016J L024), and Natural Sciences and Engineering Research Council of Canada.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Shandong Normal University, Ji’nan, 250014, China

    Xiaodi Li

  2. Institute of Data Science and Technology, Shandong Normal University, Ji’nan, 250014, China

    Xiaodi Li

  3. Department of Automation, Tsinghua University, Beijing, 100084, China

    Shiji Song

  4. Department of Mathematics and Statistics, York University, Toronto, M3J 1P3, Canada

    Jianhong Wu

Authors
  1. Xiaodi Li
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  2. Shiji Song
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  3. Jianhong Wu
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Correspondence to Shiji Song.

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Conflict of interest The authors declare that they have no conflict of interest.

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Li, X., Song, S. & Wu, J. Impulsive control of unstable neural networks with unbounded time-varying delays. Sci. China Inf. Sci. 61, 012203 (2018). https://doi.org/10.1007/s11432-017-9097-1

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  • DOI: https://doi.org/10.1007/s11432-017-9097-1

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