New techniques for solving some matrix and matrix differential equations
Matrix and matrix differential equations play an important role in system theory, control theory, stability theory of differential equations, communication systems and many other fields. In this paper, we present the solutions of non-homogeneous matrix differential equations, convolution matrix diff...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2015-03-01
|
| Series: | Ain Shams Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2090447914001130 |
| _version_ | 1818598139013103616 |
|---|---|
| author | Zeyad Abdel Aziz Al-Zhour |
| author_facet | Zeyad Abdel Aziz Al-Zhour |
| author_sort | Zeyad Abdel Aziz Al-Zhour |
| collection | DOAJ |
| description | Matrix and matrix differential equations play an important role in system theory, control theory, stability theory of differential equations, communication systems and many other fields. In this paper, we present the solutions of non-homogeneous matrix differential equations, convolution matrix differential equations and matrix equations which include the renewal matrix equation by using convolution and Kronecker products of matrices. Furthermore, the existence and uniqueness of the solution of some important and interesting special cases of these equations are also considered with some illustrated examples in order to show our new approaches. |
| first_indexed | 2024-12-16T11:58:57Z |
| format | Article |
| id | doaj.art-7dedcd5b9ecd495784a1bfa59f003b7b |
| institution | Directory Open Access Journal |
| issn | 2090-4479 |
| language | English |
| last_indexed | 2024-12-16T11:58:57Z |
| publishDate | 2015-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Ain Shams Engineering Journal |
| spelling | doaj.art-7dedcd5b9ecd495784a1bfa59f003b7b2022-12-21T22:32:30ZengElsevierAin Shams Engineering Journal2090-44792015-03-016134735410.1016/j.asej.2014.08.009New techniques for solving some matrix and matrix differential equationsZeyad Abdel Aziz Al-ZhourMatrix and matrix differential equations play an important role in system theory, control theory, stability theory of differential equations, communication systems and many other fields. In this paper, we present the solutions of non-homogeneous matrix differential equations, convolution matrix differential equations and matrix equations which include the renewal matrix equation by using convolution and Kronecker products of matrices. Furthermore, the existence and uniqueness of the solution of some important and interesting special cases of these equations are also considered with some illustrated examples in order to show our new approaches.http://www.sciencedirect.com/science/article/pii/S2090447914001130Convolution productKronecker productsMoore–Penrose inverseLeast-square problem |
| spellingShingle | Zeyad Abdel Aziz Al-Zhour New techniques for solving some matrix and matrix differential equations Ain Shams Engineering Journal Convolution product Kronecker products Moore–Penrose inverse Least-square problem |
| title | New techniques for solving some matrix and matrix differential equations |
| title_full | New techniques for solving some matrix and matrix differential equations |
| title_fullStr | New techniques for solving some matrix and matrix differential equations |
| title_full_unstemmed | New techniques for solving some matrix and matrix differential equations |
| title_short | New techniques for solving some matrix and matrix differential equations |
| title_sort | new techniques for solving some matrix and matrix differential equations |
| topic | Convolution product Kronecker products Moore–Penrose inverse Least-square problem |
| url | http://www.sciencedirect.com/science/article/pii/S2090447914001130 |
| work_keys_str_mv | AT zeyadabdelazizalzhour newtechniquesforsolvingsomematrixandmatrixdifferentialequations |