A new condition for Root Clustering in PMI regions
This paper proposes a new condition for the root clustering of a real matrix A in a complex region D defined by a polynomial matrix inequality (PMI region). For a general case, a sufficient condition is given so that the eigenvalues of A lie in D . It was shown that this condition is necessary and s...
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| Format: | Article |
| Language: | English |
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ICI Publishing House
2024-12-01
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| Series: | Revista Română de Informatică și Automatică |
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| Online Access: | https://rria.ici.ro/documents/1231/art._6_Bouazizi.pdf |
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| author | Mohamed Hechmi BOUAZIZI |
| author_facet | Mohamed Hechmi BOUAZIZI |
| author_sort | Mohamed Hechmi BOUAZIZI |
| collection | DOAJ |
| description | This paper proposes a new condition for the root clustering of a real matrix A in a complex region D defined by a polynomial matrix inequality (PMI region). For a general case, a sufficient condition is given so that the eigenvalues of A lie in D . It was shown that this condition is necessary and sufficient for some particular PMI regions including linear matrix inequality (LMI) regions, quadratic matrix inequality (QMI) regions, polynomial regions and many others.
This paper also provides an extension to the classical theorem of Cyparissos Stephanos, which formulates the relationship between the eigenvalues of two matrices and those of composite matrices of their Kronecker products. This extension turned out to be crucial for proving the main results obtained.
Based on the analysis of the proposed condition, a guardian map function can be used for tackling the problem of robust D-stability of single-parameter uncertain linear systems, for which the exact and possibly disconnected domain of D-stability was determined. All the obtained results were illustrated by certain examples. |
| format | Article |
| id | doaj-art-a095f2ed010046cd92e1861817cbe2ae |
| institution | Kabale University |
| issn | 1220-1758 1841-4303 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | ICI Publishing House |
| record_format | Article |
| series | Revista Română de Informatică și Automatică |
| spelling | doaj-art-a095f2ed010046cd92e1861817cbe2ae2025-01-20T08:00:18ZengICI Publishing HouseRevista Română de Informatică și Automatică1220-17581841-43032024-12-01344678210.33436/v34i4y202406A new condition for Root Clustering in PMI regions Mohamed Hechmi BOUAZIZI 0Higher Institute of Medical Technologies, Tunis El Manar University, Tunis, Tunisia Analysis, Conception and Control of Systems Laboratory, National Engineering School of Tunis, Tunisia This paper proposes a new condition for the root clustering of a real matrix A in a complex region D defined by a polynomial matrix inequality (PMI region). For a general case, a sufficient condition is given so that the eigenvalues of A lie in D . It was shown that this condition is necessary and sufficient for some particular PMI regions including linear matrix inequality (LMI) regions, quadratic matrix inequality (QMI) regions, polynomial regions and many others. This paper also provides an extension to the classical theorem of Cyparissos Stephanos, which formulates the relationship between the eigenvalues of two matrices and those of composite matrices of their Kronecker products. This extension turned out to be crucial for proving the main results obtained. Based on the analysis of the proposed condition, a guardian map function can be used for tackling the problem of robust D-stability of single-parameter uncertain linear systems, for which the exact and possibly disconnected domain of D-stability was determined. All the obtained results were illustrated by certain examples.https://rria.ici.ro/documents/1231/art._6_Bouazizi.pdfroot clusteringpolynomial matrix inequalitypmi regionlmi regionrobust d-stabilityuncertain systems |
| spellingShingle | Mohamed Hechmi BOUAZIZI A new condition for Root Clustering in PMI regions Revista Română de Informatică și Automatică root clustering polynomial matrix inequality pmi region lmi region robust d-stability uncertain systems |
| title | A new condition for Root Clustering in PMI regions |
| title_full | A new condition for Root Clustering in PMI regions |
| title_fullStr | A new condition for Root Clustering in PMI regions |
| title_full_unstemmed | A new condition for Root Clustering in PMI regions |
| title_short | A new condition for Root Clustering in PMI regions |
| title_sort | new condition for root clustering in pmi regions |
| topic | root clustering polynomial matrix inequality pmi region lmi region robust d-stability uncertain systems |
| url | https://rria.ici.ro/documents/1231/art._6_Bouazizi.pdf |
| work_keys_str_mv | AT mohamedhechmibouazizi anewconditionforrootclusteringinpmiregions AT mohamedhechmibouazizi newconditionforrootclusteringinpmiregions |