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A New Approach for Exponential Stability Criteria of New Certain Nonlinear Neutral Differential Equations with Mixed Time-Varying Delays

Author

Listed:
  • Janejira Tranthi

    (Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand)

  • Thongchai Botmart

    (Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand)

  • Wajaree Weera

    (Department of Mathematics, Faculty of Science, University of Phayao, Phayao 56000, Thailand)

  • Piyapong Niamsup

    (Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

Abstract

This work is concerned with the delay-dependent criteria for exponential stability analysis of neutral differential equation with a more generally interval-distributed and discrete time-varying delays. By using a novel Lyapunov–Krasovkii functional, descriptor model transformation, utilization of the Newton–Leibniz formula, and the zero equation, the criteria for exponential stability are in the form of linear matrix inequalities (LMIs). Finally, we present the effectiveness of the theoretical results in numerical examples to show less conservative conditions than the others in the literature.

Suggested Citation

  • Janejira Tranthi & Thongchai Botmart & Wajaree Weera & Piyapong Niamsup, 2019. "A New Approach for Exponential Stability Criteria of New Certain Nonlinear Neutral Differential Equations with Mixed Time-Varying Delays," Mathematics, MDPI, vol. 7(8), pages 1-18, August.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:8:p:737-:d:256963
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    References listed on IDEAS

    as
    1. Park, Ju H. & Kwon, O.M., 2008. "Stability analysis of certain nonlinear differential equation," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 450-453.
    2. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2018. "Stationary distribution and extinction of a stochastic predator–prey model with additional food and nonlinear perturbation," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 226-239.
    3. Maharajan, C. & Raja, R. & Cao, Jinde & Rajchakit, G. & Alsaedi, Ahmed, 2018. "Novel results on passivity and exponential passivity for multiple discrete delayed neutral-type neural networks with leakage and distributed time-delays," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 268-282.
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