A Cone-preserving Solution to a Nonsymmetric Riccati Equation
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| Title: | A Cone-preserving Solution to a Nonsymmetric Riccati Equation |
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| Authors: | Vladu, Emil, Rantzer, Anders |
| Contributors: | Lund University, Faculty of Engineering, LTH, Departments at LTH, Department of Automatic Control, Lunds universitet, Lunds Tekniska Högskola, Institutioner vid LTH, Institutionen för reglerteknik, Originator, Lund University, Faculty of Engineering, LTH, LTH Profile areas, LTH Profile Area: AI and Digitalization, Lunds universitet, Lunds Tekniska Högskola, LTH profilområden, LTH profilområde: AI och digitalisering, Originator, Lund University, Profile areas and other strong research environments, Strategic research areas (SRA), ELLIIT: the Linköping-Lund initiative on IT and mobile communication, Lunds universitet, Profilområden och andra starka forskningsmiljöer, Strategiska forskningsområden (SFO), ELLIIT: the Linköping-Lund initiative on IT and mobile communication, Originator, Lund University, Profile areas and other strong research environments, Lund University Profile areas, LU Profile Area: Natural and Artificial Cognition, Lunds universitet, Profilområden och andra starka forskningsmiljöer, Lunds universitets profilområden, LU profilområde: Naturlig och artificiell kognition, Originator, Lund University, Faculty of Engineering, LTH, LTH Profile areas, LTH Profile Area: The Energy Transition, Lunds universitet, Lunds Tekniska Högskola, LTH profilområden, LTH profilområde: Energiomställningen, Originator |
| Source: | Linear Algebra and Its Applications. 709:449-459 |
| Subject Terms: | Engineering and Technology, Electrical Engineering, Electronic Engineering, Information Engineering, Control Engineering, Teknik, Elektroteknik och elektronik, Reglerteknik |
| Description: | 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. |
| Access URL: | https://doi.org/10.1016/j.laa.2025.01.020 |
| Database: | SwePub |
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Nájsť tento článok vo Web of Science | Abstract: | 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. |
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| ISSN: | 18731856 |
| DOI: | 10.1016/j.laa.2025.01.020 |