Coefficient‐based conditions of matrix‐valued real‐rational proper negative imaginary functions.
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| Title: | Coefficient‐based conditions of matrix‐valued real‐rational proper negative imaginary functions. |
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| Authors: | Zhang, Qian1 (AUTHOR), Liu, Liu2 (AUTHOR) beth.liu@dlut.edu.cn, Lu, Yufeng2 (AUTHOR) |
| Source: | Asian Journal of Control. May2025, Vol. 27 Issue 3, p1594-1601. 8p. |
| Subjects: | Real variables, Numerical functions, Eigenfunctions, Matrices (Mathematics) |
| Abstract: | This paper mainly gives sufficient coefficient‐based conditions of matrix‐valued real‐rational proper negative imaginary (NI) functions. The proper NI functions can be divided into three cases by relative order, namely, NI functions with relative order 0, 1, and 2. Based on the relationship between NI functions with poles at 0 and without poles at 0, as well as coefficient‐based conditions of positive real functions, sufficient coefficient‐based conditions are shown of NI functions with relative order 1 and 2. These main results are related to the numerical radius and Crawford number of matrices. Moreover, they are supplements to some existing results. NI functions with relative order 0 can be changed into the case of relative order 1, and the sufficient coefficient‐based conditions are also obtained of NI functions with relative order 0. In addition, the coefficient‐based conditions can be used to construct interval NI functions, and some examples are given to illustrate the main results. [ABSTRACT FROM AUTHOR] |
| Copyright of Asian Journal of Control is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 185185771 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Coefficient‐based conditions of matrix‐valued real‐rational proper negative imaginary functions. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Zhang%2C+Qian%22">Zhang, Qian</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Liu%2C+Liu%22">Liu, Liu</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> beth.liu@dlut.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Lu%2C+Yufeng%22">Lu, Yufeng</searchLink><relatesTo>2</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Asian+Journal+of+Control%22">Asian Journal of Control</searchLink>. May2025, Vol. 27 Issue 3, p1594-1601. 8p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Real+variables%22">Real variables</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+functions%22">Numerical functions</searchLink><br /><searchLink fieldCode="DE" term="%22Eigenfunctions%22">Eigenfunctions</searchLink><br /><searchLink fieldCode="DE" term="%22Matrices+%28Mathematics%29%22">Matrices (Mathematics)</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper mainly gives sufficient coefficient‐based conditions of matrix‐valued real‐rational proper negative imaginary (NI) functions. The proper NI functions can be divided into three cases by relative order, namely, NI functions with relative order 0, 1, and 2. Based on the relationship between NI functions with poles at 0 and without poles at 0, as well as coefficient‐based conditions of positive real functions, sufficient coefficient‐based conditions are shown of NI functions with relative order 1 and 2. These main results are related to the numerical radius and Crawford number of matrices. Moreover, they are supplements to some existing results. NI functions with relative order 0 can be changed into the case of relative order 1, and the sufficient coefficient‐based conditions are also obtained of NI functions with relative order 0. In addition, the coefficient‐based conditions can be used to construct interval NI functions, and some examples are given to illustrate the main results. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Asian Journal of Control is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1002/asjc.3521 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 8 StartPage: 1594 Subjects: – SubjectFull: Real variables Type: general – SubjectFull: Numerical functions Type: general – SubjectFull: Eigenfunctions Type: general – SubjectFull: Matrices (Mathematics) Type: general Titles: – TitleFull: Coefficient‐based conditions of matrix‐valued real‐rational proper negative imaginary functions. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Zhang, Qian – PersonEntity: Name: NameFull: Liu, Liu – PersonEntity: Name: NameFull: Lu, Yufeng IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Text: May2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 15618625 Numbering: – Type: volume Value: 27 – Type: issue Value: 3 Titles: – TitleFull: Asian Journal of Control Type: main |
| ResultId | 1 |
