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

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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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Authors and Affiliations

  1. Department of Mathematics, University of Sciences, Hue University, 77 Nguyen Hue Road, Hue, Vietnam

    Le A. Tuan

  2. Institute of Mathematics, VAST, 18 Hoang Quoc Viet Road, Hanoi, 10307, Vietnam

    Vu N. Phat

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  1. Le A. Tuan
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  2. Vu N. Phat
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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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  • DOI: https://doi.org/10.1007/s40840-018-0608-y

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