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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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Correspondence to Shiji Song.

Additional information

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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Keywords

  • unstable neural networks
  • impulsive control
  • unbounded discrete time-varying delay
  • unbounded distributed time-varying delay
  • μ-stability