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Exponential Stability of Nonlinear Time-Varying Delay Differential Equations via Lyapunov–Razumikhin Technique

Author

Listed:
  • Natalya O. Sedova

    (Department of Mathematics, Information and Aviation Technology, Ulyanovsk State University, 432017 Ulyanovsk, Russia)

  • Olga V. Druzhinina

    (Federal Research Center “Computer Science and Control” of Russian Academy of Sciences, 119333 Moscow, Russia
    V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 117997 Moscow, Russia)

Abstract

In this article, some new sufficient conditions for the exponential stability of nonlinear time-varying delay differential equations are given. An extension of the classical asymptotical stability theorem in terms of a Lyapunov–Razumikhin function is obtained. The condition of non-positivity of the time derivative of a Razumikhin function is weakened. Additionally, the resulting sufficient asymptotic stability conditions allow us to guarantee uniform exponential stability and evaluate the exponential convergence rate of the system solutions. The effectiveness of the results is demonstrated by some examples.

Suggested Citation

  • Natalya O. Sedova & Olga V. Druzhinina, 2023. "Exponential Stability of Nonlinear Time-Varying Delay Differential Equations via Lyapunov–Razumikhin Technique," Mathematics, MDPI, vol. 11(4), pages 1-15, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:896-:d:1063996
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    References listed on IDEAS

    as
    1. Wei Hu, 2022. "Stability of Impulsive Stochastic Delay Systems with Markovian Switched Delay Effects," Mathematics, MDPI, vol. 10(7), pages 1-12, March.
    2. Branislav Rehák & Volodymyr Lynnyk, 2021. "Synchronization of a Network Composed of Stochastic Hindmarsh–Rose Neurons," Mathematics, MDPI, vol. 9(20), pages 1-16, October.
    3. Zihan Zou & Yinfang Song & Chi Zhao, 2022. "Razumikhin Theorems on Polynomial Stability of Neutral Stochastic Pantograph Differential Equations with Markovian Switching," Mathematics, MDPI, vol. 10(17), pages 1-15, August.
    4. Ruofeng Rao & Zhi Lin & Xiaoquan Ai & Jiarui Wu, 2022. "Synchronization of Epidemic Systems with Neumann Boundary Value under Delayed Impulse," Mathematics, MDPI, vol. 10(12), pages 1-10, June.
    5. Mao, Xuerong, 1996. "Razumikhin-type theorems on exponential stability of stochastic functional differential equations," Stochastic Processes and their Applications, Elsevier, vol. 65(2), pages 233-250, December.
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