Negative imaginary lemmas for improper descriptor systems
This paper studies the negative imaginary property for improper descriptor systems. Firstly, it is demonstrated that a descriptor system with a negative imaginary transfer function cannot be impulse-free, that is, the negative imaginary transfer function is improper. Then some necessary conditions a...
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| Published in | Journal of the Franklin Institute Vol. 362; no. 8; p. 107690 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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Elsevier Inc
15.05.2025
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| Online Access | Get full text |
| ISSN | 0016-0032 |
| DOI | 10.1016/j.jfranklin.2025.107690 |
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| Abstract | This paper studies the negative imaginary property for improper descriptor systems. Firstly, it is demonstrated that a descriptor system with a negative imaginary transfer function cannot be impulse-free, that is, the negative imaginary transfer function is improper. Then some necessary conditions and sufficient conditions are established to characterize the negative imaginary property of improper descriptor systems based on the quasi-Weierstrass form. Furthermore, the lossless negative imaginary property of improper descriptor systems is derived by the relationship between the lossless positive realness and the lossless negative imaginariness. Several examples are given to illustrate the obtained results. In addition, this paper presents a generalized Kalman–Yakubovich–Popov lemma for the negative imaginary property of descriptor systems, which is achieved independently of the relationship between positive realness and negative imaginariness. |
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| AbstractList | This paper studies the negative imaginary property for improper descriptor systems. Firstly, it is demonstrated that a descriptor system with a negative imaginary transfer function cannot be impulse-free, that is, the negative imaginary transfer function is improper. Then some necessary conditions and sufficient conditions are established to characterize the negative imaginary property of improper descriptor systems based on the quasi-Weierstrass form. Furthermore, the lossless negative imaginary property of improper descriptor systems is derived by the relationship between the lossless positive realness and the lossless negative imaginariness. Several examples are given to illustrate the obtained results. In addition, this paper presents a generalized Kalman–Yakubovich–Popov lemma for the negative imaginary property of descriptor systems, which is achieved independently of the relationship between positive realness and negative imaginariness. |
| ArticleNumber | 107690 |
| Author | Gao, Meiqi Gan, Naifeng Liu, Xiaolu Liu, Liu |
| Author_xml | – sequence: 1 givenname: Xiaolu orcidid: 0000-0003-0822-4669 surname: Liu fullname: Liu, Xiaolu organization: School of Mathematical Sciences, Dalian University of Technology, Dalian, China – sequence: 2 givenname: Meiqi surname: Gao fullname: Gao, Meiqi organization: School of Mathematical Sciences, Dalian University of Technology, Dalian, China – sequence: 3 givenname: Liu surname: Liu fullname: Liu, Liu email: beth.liu@dlut.edu.cn organization: School of Mathematical Sciences, Dalian University of Technology, Dalian, China – sequence: 4 givenname: Naifeng surname: Gan fullname: Gan, Naifeng organization: School of Mathematics and Statistics, Lingnan normal university, Zhanjiang, China |
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| Cites_doi | 10.1109/TAC.2020.2994180 10.1109/TAC.2014.2325692 10.1109/TAC.2004.840475 10.1137/060669061 10.1109/TAC.2008.919567 10.1016/j.jfranklin.2023.11.028 10.1016/j.laa.2012.12.044 10.1016/j.sysconle.2015.10.008 10.1016/j.sysconle.2015.09.003 10.1016/j.jfranklin.2019.11.071 10.1109/TAC.2010.2052711 10.1007/s00498-023-00373-2 10.1002/rnc.4231 10.1016/j.automatica.2024.111742 10.1109/TAC.1981.1102763 10.1080/10556780410001654232 10.1016/j.laa.2009.12.036 10.1016/j.automatica.2022.110634 10.1016/j.sysconle.2015.01.008 10.1109/81.989180 10.1016/j.automatica.2020.109079 |
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