Quantitatively hyper-positive real rational functions III
Optimization and Control
2026-03-02 v1
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.
Cite
@article{arxiv.2602.23695,
title = {Quantitatively hyper-positive real rational functions III},
author = {Daniel Alpay and Izchak Lewkowicz},
journal= {arXiv preprint arXiv:2602.23695},
year = {2026}
}