Global Asymptotic Stabilization of Cellular Neural Networks with Proportional Delay via Impulsive Control

Abstract

This paper considers the global asymptotic stabilization of a class of cellular neural networks with proportional delay via impulsive control. First, from impulsive control point of view, some delay-dependent criteria are established to guarantee the asymptotic stability and global asymptotic stability of the zero solution of a general impulsive differential system with proportional delay by applying the Lyapunov–Razumikhin method. Second, based on the obtained criteria and LMI approach, several delay-dependent conditions are derived to ensure the uniqueness and global asymptotic stability of the equilibrium point of a class of cellular neural networks with impulses and proportional delay. It is shown that impulses can be used to globally asymptotically stabilize some unstable and even chaotic cellular neural networks with proportional delay. Moreover, the proposed stability conditions expressed in terms of linear matrix inequalities (LMIs) can be checked by the Matlab LMI toolbox, and so it is effective to implement in real problems. Finally, three numerical examples are provided to illustrate the effectiveness of the theoretical results.

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Acknowledgements

The authors would like to thank the editor and the anonymous reviewers for a number of valuable comments and constructive suggestions that have improved the presentation and quality of this paper. This work was supported by the Natural Science Foundation of Guangdong Province, China (Nos. 2016A030313005 and 2015A030313643) and the Innovation Project of Department of Education of Guangdong Province, China (No. 2015KTSCX147).

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Correspondence to Kaizhong Guan.

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Guan, K., Yang, J. Global Asymptotic Stabilization of Cellular Neural Networks with Proportional Delay via Impulsive Control. Neural Process Lett 50, 1969–1992 (2019). https://doi.org/10.1007/s11063-019-09980-0

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Keywords

  • Global asymptotic stability
  • Cellular neural network
  • Proportional delay
  • Impulsive control
  • Lyapunov–Razumikhin method
  • Linear matrix inequality (LMI)

Mathematics Subject Classification

  • 34D23
  • 93D20