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Indefinite derivative Lyapunov–Krasovskii functional method for input to state stability of nonlinear systems with time-delay

Author

Listed:
  • Ning, Chongyang
  • He, Yong
  • Wu, Min
  • Zhou, Shaowu

Abstract

In this paper, the problem of the input to state stability (ISS) for nonlinear systems with time-delay is investigated. A continuously differentiable Lyapunov–Krasovskii functional with indefinite derivative is introduced to derive the ISS of the systems, which generalizes the classic Lyapunov–Krasovskii functional with positive definite derivative. As a result, the uniform stability and uniform asymptotic stability criteria of nonlinear systems with time-delay are also established by employing the proposed Lyapunov–Krasovskii functional.

Suggested Citation

  • Ning, Chongyang & He, Yong & Wu, Min & Zhou, Shaowu, 2015. "Indefinite derivative Lyapunov–Krasovskii functional method for input to state stability of nonlinear systems with time-delay," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 534-542.
    • Handle: RePEc:eee:apmaco:v:270:y:2015:i:c:p:534-542
    DOI: 10.1016/j.amc.2015.08.063
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    Cited by:

    1. Li, Peng & Li, Xiaodi, 2019. "Input-to-state stability of nonlinear impulsive systems via Lyapunov method involving indefinite derivative," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 314-323.
    2. Peng Li & Xiaodi Li & Jinde Cao, 2018. "Input-to-State Stability of Nonlinear Switched Systems via Lyapunov Method Involving Indefinite Derivative," Complexity, Hindawi, vol. 2018, pages 1-8, January.

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