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DOI: 10.23952/cot.2024.30
Received September 24, 2023; Accepted December 12, 2023; Published online May 16, 2024
Abstract. In this paper, we consider the problem of existence of an affine parameter-dependent quadratic Lyapunov functions for a matrix segment. It is assumed that this segment is robustly Hurwitz stable. A sufficient condition for the existence of such a function is given. Concerning Barmish’s conjecture, we give an explicit algorithm for the calculation of the matrices which play a key role in the counterexample. One conjecture on 2 x 2 matrix segments is provided.
How to Cite this Article:
T. Büyükköroğlu, B. Aksoy, V. Dzhafarov, On existence of affine parameter-dependent lyapunov functions, Commun. Optim. Theory 2024 (2024) 30.