Common Solutions to Stein Inequalities
In this paper for linear discrete time switched systems, the problem of existence of a common solution to Stein inequalities is considered. A sufficient condition for robust Schur stability of a matrix polyope by using Schur complement lemma and a necessary and sufficient condition for the existence...
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| Format: | Article |
| Language: | English |
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Sakarya University
2023-10-01
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| Series: | Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi |
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| Online Access: | https://dergipark.org.tr/tr/download/article-file/2990917 |
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| _version_ | 1846111332458299392 |
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| author | Birgül Aksoy Şerife Yılmaz |
| author_facet | Birgül Aksoy Şerife Yılmaz |
| author_sort | Birgül Aksoy |
| collection | DOAJ |
| description | In this paper for linear discrete time switched systems, the problem of existence of a common solution to Stein inequalities is considered. A sufficient condition for robust Schur stability of a matrix polyope by using Schur complement lemma and a necessary and sufficient condition for the existence of a common solution of Stein equation are given. As in the case of continuous time systems, the problem of existence of a common solution is reduced to a convex optimization one. An efficient solution algorithm which requires solving a linear minimax problem at each step is suggested. The algorithm is supported with a number of examples from the literature and observed that the method desired results fastly. |
| format | Article |
| id | doaj-art-742a7043d49e49bd82cc0486a0089305 |
| institution | Kabale University |
| issn | 2147-835X |
| language | English |
| publishDate | 2023-10-01 |
| publisher | Sakarya University |
| record_format | Article |
| series | Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi |
| spelling | doaj-art-742a7043d49e49bd82cc0486a00893052024-12-23T08:15:40ZengSakarya UniversitySakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi2147-835X2023-10-012751097110310.16984/saufenbilder.126043828Common Solutions to Stein InequalitiesBirgül Aksoyhttps://orcid.org/0000-0002-9502-3648Şerife Yılmaz0https://orcid.org/0000-0002-7561-3288BURDUR MEHMET AKİF ERSOY ÜNİVERSİTESİIn this paper for linear discrete time switched systems, the problem of existence of a common solution to Stein inequalities is considered. A sufficient condition for robust Schur stability of a matrix polyope by using Schur complement lemma and a necessary and sufficient condition for the existence of a common solution of Stein equation are given. As in the case of continuous time systems, the problem of existence of a common solution is reduced to a convex optimization one. An efficient solution algorithm which requires solving a linear minimax problem at each step is suggested. The algorithm is supported with a number of examples from the literature and observed that the method desired results fastly.https://dergipark.org.tr/tr/download/article-file/2990917discrete-time systemschur stabilitystein equationcommon quadratic lyapunov functionschur complement |
| spellingShingle | Birgül Aksoy Şerife Yılmaz Common Solutions to Stein Inequalities Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi discrete-time system schur stability stein equation common quadratic lyapunov function schur complement |
| title | Common Solutions to Stein Inequalities |
| title_full | Common Solutions to Stein Inequalities |
| title_fullStr | Common Solutions to Stein Inequalities |
| title_full_unstemmed | Common Solutions to Stein Inequalities |
| title_short | Common Solutions to Stein Inequalities |
| title_sort | common solutions to stein inequalities |
| topic | discrete-time system schur stability stein equation common quadratic lyapunov function schur complement |
| url | https://dergipark.org.tr/tr/download/article-file/2990917 |
| work_keys_str_mv | AT birgulaksoy commonsolutionstosteininequalities AT serifeyılmaz commonsolutionstosteininequalities |