Converse Lyapunov Results for Uniform Stability Properties

Ihab Haidar () and Paolo Mason ()
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Ihab Haidar: Laboratoire Quartz EA 7393, ENSEA
Paolo Mason: Laboratoire des Signaux et Systèmes, Université Paris-Saclay, CNRS, CentraleSupélec

Journal of Optimization Theory and Applications, 2025, vol. 206, issue 2, No 18, 30 pages

Abstract: Abstract Converse Lyapunov results express the fact that, for a given dynamical model, the existence of a Lyapunov function is not only a sufficient condition for its stability, but also a necessary criterion. These results provide a solid justification for the Lyapunov approach as a tool to investigate stability, and also make it possible to prove auxiliary robustness properties of dynamical systems. This survey presents converse Lyapunov results concerned with uniform asymptotic stability of dynamical systems in the presence of parametric perturbations, giving a particular emphasis to the infinite-dimensional case.

Keywords: Uniform asymptotic stability; Converse Lyapunov results; 93D09; 93D20; 93D30 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02698-1

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