Quantitatively hyper-positive real rational functions III

Daniel Alpay; Izchak Lewkowicz

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arXiv · 2602.23695

Quantitatively hyper-positive real rational functions III

Daniel Alpay·Izchak Lewkowicz

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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.

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Daniel Alpay, Izchak Lewkowicz. 2026-02-27. Quantitatively hyper-positive real rational functions III. https://arxiv.org/abs/2602.23695

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