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

  • Xiaodi Li
  • Shiji SongEmail author
  • Jianhong Wu
Research Paper


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.


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



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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Copyright information

© Science China Press and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsShandong Normal UniversityJi’nanChina
  2. 2.Institute of Data Science and TechnologyShandong Normal UniversityJi’nanChina
  3. 3.Department of AutomationTsinghua UniversityBeijingChina
  4. 4.Department of Mathematics and StatisticsYork UniversityTorontoCanada

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