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

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.

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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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Correspondence to Vu N. Phat.

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Communicated by Syakila Ahmad.

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Tuan, L.A., Phat, V.N. Existence of Solutions and Finite-Time Stability for Nonlinear Singular Discrete-Time Neural Networks. Bull. Malays. Math. Sci. Soc. 42, 2423–2442 (2019). https://doi.org/10.1007/s40840-018-0608-y

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Keywords

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

Mathematics Subject Classification

  • 34D06
  • 65L20
  • 93D20
  • 94D05