On the numerical verification of a counterexample on parameter-dependent Lyapunov functions

Birgül Aksoy, Taner Büyükköroğlu and Vakif Dzhafarov

Applied Mathematics and Computation, 2025, vol. 492, issue C

Abstract: We consider the existence problem of an affine parameter-dependent quadratic Lyapunov function for a robust Hurwitz stable matrix segment. Numerical verification of the known counterexample to the known Barmish's conjecture is provided. Second order parameter-dependent quadratic Lyapunov function for this counterexample is constructed. Sufficient conditions for the existence of an affine parameter-dependent Lyapunov function are given.

Keywords: Hurwitz stability; Matrix segment; Common Lyapunov function; Linear matrix inequality (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:492:y:2025:i:c:s0096300324007070

DOI: 10.1016/j.amc.2024.129246

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