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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Main Authors: Birgül Aksoy, Şerife Yılmaz
Format: Article
Language:English
Published: Sakarya University 2023-10-01
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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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