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Building coercive Lyapunov-Krasovskii functionals based on Razumikhin and Halanay approaches
  • Antoine Chaillet,
  • Epiphane Loko,
  • Iasson Karafyllis
Antoine Chaillet
Laboratoire des Signaux et Systemes

Corresponding Author:[email protected]

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Epiphane Loko
Laboratoire des Signaux et Systemes
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Iasson Karafyllis
National Technical University of Athens
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In this paper, we provide a systematic and constructive way to build a Lyapunov-Krasovskii functional for time-delay systems whose stability can be established through the Razumikhin or the Halanay approaches. The constructed Lyapunov-Krasovskii functional turns out to be coercive, meaning sandwiched between functions of the state history norm, and to dissipate in terms of the whole history norm. We present these results in the framework of input-to-state stability (ISS) in order to further account for the influence of input disturbances. A special emphasis is also given on exponential stability and exponential ISS. We illustrate our findings though the study of a coupled ODE-PDE model of a chemical reactor, and show that, unlike most results in that area, our approach happens to ensure ISS in terms of the supremum norm of the state.
07 Jul 2023Submitted to International Journal of Robust and Nonlinear Control
07 Jul 2023Submission Checks Completed
07 Jul 2023Assigned to Editor
07 Jul 2023Review(s) Completed, Editorial Evaluation Pending
07 Jul 2023Reviewer(s) Assigned
15 Sep 2023Editorial Decision: Revise Minor
07 Nov 20231st Revision Received
11 Nov 2023Submission Checks Completed
11 Nov 2023Assigned to Editor
11 Nov 2023Review(s) Completed, Editorial Evaluation Pending
13 Nov 2023Reviewer(s) Assigned