Stability Analysis of an LTI System with Diagonal Norm Bounded Linear Differential Inclusions
In this article, we present a stability analysis of linear time-invariant systems in control theory. The linear time-invariant systems under consideration involve the diagonal norm bounded linear differential inclusions. We propose a methodology based on low-rank ordinary differential equations. We...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-01-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/1/152 |
| _version_ | 1797409964471353344 |
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| author | Mutti-Ur Rehman Sohail Iqbal Jehad Alzabut Rami Ahmad El-Nabulsi |
| author_facet | Mutti-Ur Rehman Sohail Iqbal Jehad Alzabut Rami Ahmad El-Nabulsi |
| author_sort | Mutti-Ur Rehman |
| collection | DOAJ |
| description | In this article, we present a stability analysis of linear time-invariant systems in control theory. The linear time-invariant systems under consideration involve the diagonal norm bounded linear differential inclusions. We propose a methodology based on low-rank ordinary differential equations. We construct an equivalent time-invariant system (linear) and use it to acquire an optimization problem whose solutions are given in terms of a system of differential equations. An iterative method is then used to solve the system of differential equations. The stability of linear time-invariant systems with diagonal norm bounded differential inclusion is studied by analyzing the Spectrum of equivalent systems. |
| first_indexed | 2024-03-09T04:22:06Z |
| format | Article |
| id | doaj.art-9186f19a45fd4c16b0a8d0a3b5537552 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T04:22:06Z |
| publishDate | 2021-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-9186f19a45fd4c16b0a8d0a3b55375522023-12-03T13:45:49ZengMDPI AGSymmetry2073-89942021-01-0113115210.3390/sym13010152Stability Analysis of an LTI System with Diagonal Norm Bounded Linear Differential InclusionsMutti-Ur Rehman0Sohail Iqbal1Jehad Alzabut2Rami Ahmad El-Nabulsi3Department of Mathematics, Sukkur IBA University, Sukkur 65200, PakistanDepartment of Mathematics, COMSATS University Islamabad, Islamabad Campus, Islamabad 44000, PakistanDepartment of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaAthens Institute for Education and Research, Mathematics and Physics Divisions, 8 Valaoritou Street, Kolonaki, 10671 Athens, GreeceIn this article, we present a stability analysis of linear time-invariant systems in control theory. The linear time-invariant systems under consideration involve the diagonal norm bounded linear differential inclusions. We propose a methodology based on low-rank ordinary differential equations. We construct an equivalent time-invariant system (linear) and use it to acquire an optimization problem whose solutions are given in terms of a system of differential equations. An iterative method is then used to solve the system of differential equations. The stability of linear time-invariant systems with diagonal norm bounded differential inclusion is studied by analyzing the Spectrum of equivalent systems.https://www.mdpi.com/2073-8994/13/1/152linear differential inclusionspectrum of an operatordifferential equations |
| spellingShingle | Mutti-Ur Rehman Sohail Iqbal Jehad Alzabut Rami Ahmad El-Nabulsi Stability Analysis of an LTI System with Diagonal Norm Bounded Linear Differential Inclusions Symmetry linear differential inclusion spectrum of an operator differential equations |
| title | Stability Analysis of an LTI System with Diagonal Norm Bounded Linear Differential Inclusions |
| title_full | Stability Analysis of an LTI System with Diagonal Norm Bounded Linear Differential Inclusions |
| title_fullStr | Stability Analysis of an LTI System with Diagonal Norm Bounded Linear Differential Inclusions |
| title_full_unstemmed | Stability Analysis of an LTI System with Diagonal Norm Bounded Linear Differential Inclusions |
| title_short | Stability Analysis of an LTI System with Diagonal Norm Bounded Linear Differential Inclusions |
| title_sort | stability analysis of an lti system with diagonal norm bounded linear differential inclusions |
| topic | linear differential inclusion spectrum of an operator differential equations |
| url | https://www.mdpi.com/2073-8994/13/1/152 |
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