关于Lyapunov和Riccati不等式在锥上准单调（QM）映射扩散解的注记
A note on diffusive solutions of the Lyapunov and Riccati inequalities for quasi-monotone (QM) mappings on cones
AI总结：
本文研究了准单调映射在锥上的扩散解，扩展了Lyapunov和Riccati不等式的稳定性概念，并探讨了与对称锥相关的结果。
摘要：
我们考虑Metzler和非负矩阵的三个关键性质及其对自对偶proper凸锥类的扩展。具体而言，我们研究相对于锥$K$准单调（QM）的映射，并讨论将D稳定性、对角Lyapunov稳定性以及对角Riccati稳定性扩展到此设定的结果。相对于锥作用扩散的映射被用作对角矩阵的推广。还讨论了使用Jordan代数方法获得的对称锥近期结果之间的关系。
英文摘要：
We consider three key properties of Metzler and nonnegative matrices and extensions of these to 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
