Quantitatively Hyper-Positive Real Rational Functions III

Authors

• Daniel Alpay, Chapman UniversityFollow
• Izchak Lewkowicz, Ben-Gurion University of the Negev

Document Type

Article

Publication Date

6-5-2026

Abstract

Hyper-Positive Real, matrix-valued, rational functions are associated with absolute stability (the Lurie problem). Here, quantitative subsets of Hyper-positive functions, related through nested inclusions, are introduced. Structurally, this family of functions turns out to be matrix-convex and closed under inversion. A state-space characterization of these functions through a corresponding Kalman-Yakubovich-Popov Lemma, is given. Technically, the classical Linear Matrix Inclusions, associated with passive systems, are here substituted by Quadratic Matrix Inclusions.

Comments

This article was originally published in Linear Algebra and its Applications, volume 747, in 2026. https://doi.org/10.1016/j.laa.2026.06.001

Recommended Citation

D. Alpay, I. Lewkowicz, Quantitatively hyper-positive real rational functions III, Linear Algebra Appl. 747 (2026) 166-208. https://doi.org/10.1016/j.laa.2026.06.001

Peer Reviewed

1

Copyright

The authors

Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.