A Cone-preserving Solution to a Nonsymmetric Riccati Equation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917875924598784 |
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| author | Vladu, Emil Rantzer, Anders |
| author_facet | Vladu, Emil Rantzer, Anders |
| contents | In this paper, we provide the following simple equivalent condition for a nonsymmetric Algebraic Riccati Equation to admit a stabilizing cone-preserving solution: an associated coefficient matrix must be stable. The result holds under the assumption that said matrix be cross-positive on a proper cone, and it both extends and completes a corresponding sufficient condition for nonnegative matrices in the literature. Further, key to showing the above is the following result which we also provide: in order for a monotonically increasing sequence of cone-preserving matrices to converge, it is sufficient to be bounded above in a single vectorial direction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14470 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Cone-preserving Solution to a Nonsymmetric Riccati Equation Vladu, Emil Rantzer, Anders Optimization and Control In this paper, we provide the following simple equivalent condition for a nonsymmetric Algebraic Riccati Equation to admit a stabilizing cone-preserving solution: an associated coefficient matrix must be stable. The result holds under the assumption that said matrix be cross-positive on a proper cone, and it both extends and completes a corresponding sufficient condition for nonnegative matrices in the literature. Further, key to showing the above is the following result which we also provide: in order for a monotonically increasing sequence of cone-preserving matrices to converge, it is sufficient to be bounded above in a single vectorial direction. |
| title | A Cone-preserving Solution to a Nonsymmetric Riccati Equation |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2411.14470 |