New Results on Stability for a Class of Fractional-Order Static Neural Networks

Abstract

This paper investigates the stability of a class of fractional-order static neural networks. Two new Lyapunov functions with proper integral terms are constructed. These integrals with variable upper limit are convex functions. Based on the fractional-order Lyapunov direct method and some inequality skills, several novel stability sufficient conditions which ensure the global Mittag–Leffler stability of fractional-order projection neural networks (FPNNs) are presented in the forms of linear matrix inequalities (LMIs). Two LMI-based Mittag–Leffler stability criteria with less conservativeness are given for a special kind of FPNNs. Finally, the effectiveness of the proposed method is demonstrated via four numerical examples.

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Acknowledgements

The authors would like to thank the editor and anonymous reviewers for their valuable comments and suggestions.

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Correspondence to Meilan Tang or Xinge Liu.

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This work is partly supported by the National Science Foundation of China under Grants 61773404 and 11601104 and Fundamental Research Funds for the Central Universities of Central South University 2018zzts316.

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Yao, X., Tang, M., Wang, F. et al. New Results on Stability for a Class of Fractional-Order Static Neural Networks. Circuits Syst Signal Process (2020). https://doi.org/10.1007/s00034-020-01451-5

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Keywords

  • Fractional-order
  • Projection neural networks
  • Convex Lyapunov function
  • Mittag–Leffler stability
  • Linear matrix inequality