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DOI: 10.23952/cot.2025.9
Received November 27, 2023; Accepted April 3, 2024; Published online Novemer 25, 2024
Abstract. We consider three key properties of Metzler and nonnegative matrices and extensions of these to mappings on classes of self-dual proper convex cones. Specifically, we study mappings that are quasi-monotone (QM) with respect to a cone K and discuss results extending D-stability, diagonal Lyapunov stability, and diagonal Riccati stability to this setting. Mappings that act diffusively with respect to the cone are used as generalisations of diagonal matrices. Relationships with recent results for symmetric cones obtained using Jordan algebraic methods are also discussed.
How to Cite this Article:
O. Mason, A note on diffusive solutions of the Lyapunov and Riccati inequalities for quasi-monotone (QM) mappings on cones, Commun. Optim. Theory 2025 (2025) 9.