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

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 functi...

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Bibliographic Details
Published in:Applied mathematics and computation 2025-05, Vol.492, Article 129246
Main Authors: Aksoy, Birgül, Büyükköroğlu, Taner, Dzhafarov, Vakif
Format: Article
Language:English
Subjects:
Common Lyapunov function
Hurwitz stability
Linear matrix inequality
Matrix segment
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Summary: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.
ISSN:0096-3003
DOI:10.1016/j.amc.2024.129246