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Existence of Solutions and Finite-Time Stability for Nonlinear Singular Discrete-Time Neural Networks

  • Le A. Tuan
  • Vu N. PhatEmail author
Article

Abstract

This paper investigates the problem of finite-time stability and control for a class of nonlinear singular discrete-time neural networks with time-varying delays and disturbances. First, based on the implicit function theorem and singular value decomposition method, a sufficient condition for the existence of the solution of such systems is established in terms of a linear matrix inequality (LMI). Then, using the Lyapunov functional approach combined with LMI technique we provide new delay-dependent sufficient conditions for robust \(H_{\infty }\) finite-time stability and control. Finally, some numerical examples are given to illustrate the efficiency of the proposed results.

Keywords

Finite-time stability Stabilization Singularity Discrete-time systems Time-varying delays Linear matrix inequalities 

Mathematics Subject Classification

34D06 65L20 93D20 94D05 

Notes

Acknowledgements

This work was supported by the National Foundation for Science and Technology Development, Vietnam, Grant 101.01.2017.300. The authors wish to thank anonymous reviewers for valuable comments and suggestions, which allowed us to improve the paper.

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2018

Authors and Affiliations

  1. 1.Department of Mathematics, University of SciencesHue UniversityHueVietnam
  2. 2.Institute of MathematicsVASTHanoiVietnam

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