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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| Accès en ligne: | https://arxiv.org/abs/2602.23695 |
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| _version_ | 1866912930010759168 |
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| author | Alpay, Daniel Lewkowicz, Izchak |
| author_facet | Alpay, Daniel Lewkowicz, Izchak |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23695 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantitatively hyper-positive real rational functions III Alpay, Daniel Lewkowicz, Izchak Optimization and Control 15A63 34H05 47A63 47N70 93B20 93C15 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. |
| title | Quantitatively hyper-positive real rational functions III |
| topic | Optimization and Control 15A63 34H05 47A63 47N70 93B20 93C15 |
| url | https://arxiv.org/abs/2602.23695 |