On the Solution of the Eigenvalue Assignment Problem for Discrete-Time Systems
The output feedback eigenvalue assignment problem for discrete-time systems is considered. The problem is formulated first as an unconstrained minimization problem, where a three-term nonlinear conjugate gradient method is proposed to find a local solution. In addition, a cut to the objective functi...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2017/7256769 |
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| author | El-Sayed M. E. Mostafa Abdallah W. Aboutahoun Fatma F. S. Omar |
| author_facet | El-Sayed M. E. Mostafa Abdallah W. Aboutahoun Fatma F. S. Omar |
| author_sort | El-Sayed M. E. Mostafa |
| collection | DOAJ |
| description | The output feedback eigenvalue assignment problem for discrete-time systems is considered. The problem is formulated first as an unconstrained minimization problem, where a three-term nonlinear conjugate gradient method is proposed to find a local solution. In addition, a cut to the objective function is included, yielding an inequality constrained minimization problem, where a logarithmic barrier method is proposed for finding the local solution. The conjugate gradient method is further extended to tackle the eigenvalue assignment problem for the two cases of decentralized control systems and control systems with time delay. The performance of the methods is illustrated through various test examples. |
| format | Article |
| id | doaj-art-26a0ddce66d94b4b98f837dc12cf594a |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-26a0ddce66d94b4b98f837dc12cf594a2025-02-03T05:53:48ZengWileyJournal of Applied Mathematics1110-757X1687-00422017-01-01201710.1155/2017/72567697256769On the Solution of the Eigenvalue Assignment Problem for Discrete-Time SystemsEl-Sayed M. E. Mostafa0Abdallah W. Aboutahoun1Fatma F. S. Omar2Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Moharam Bek, Alexandria 21511, EgyptDepartment of Mathematics and Computer Science, Faculty of Science, Alexandria University, Moharam Bek, Alexandria 21511, EgyptDepartment of Mathematics and Computer Science, Faculty of Science, Alexandria University, Moharam Bek, Alexandria 21511, EgyptThe output feedback eigenvalue assignment problem for discrete-time systems is considered. The problem is formulated first as an unconstrained minimization problem, where a three-term nonlinear conjugate gradient method is proposed to find a local solution. In addition, a cut to the objective function is included, yielding an inequality constrained minimization problem, where a logarithmic barrier method is proposed for finding the local solution. The conjugate gradient method is further extended to tackle the eigenvalue assignment problem for the two cases of decentralized control systems and control systems with time delay. The performance of the methods is illustrated through various test examples.http://dx.doi.org/10.1155/2017/7256769 |
| spellingShingle | El-Sayed M. E. Mostafa Abdallah W. Aboutahoun Fatma F. S. Omar On the Solution of the Eigenvalue Assignment Problem for Discrete-Time Systems Journal of Applied Mathematics |
| title | On the Solution of the Eigenvalue Assignment Problem for Discrete-Time Systems |
| title_full | On the Solution of the Eigenvalue Assignment Problem for Discrete-Time Systems |
| title_fullStr | On the Solution of the Eigenvalue Assignment Problem for Discrete-Time Systems |
| title_full_unstemmed | On the Solution of the Eigenvalue Assignment Problem for Discrete-Time Systems |
| title_short | On the Solution of the Eigenvalue Assignment Problem for Discrete-Time Systems |
| title_sort | on the solution of the eigenvalue assignment problem for discrete time systems |
| url | http://dx.doi.org/10.1155/2017/7256769 |
| work_keys_str_mv | AT elsayedmemostafa onthesolutionoftheeigenvalueassignmentproblemfordiscretetimesystems AT abdallahwaboutahoun onthesolutionoftheeigenvalueassignmentproblemfordiscretetimesystems AT fatmafsomar onthesolutionoftheeigenvalueassignmentproblemfordiscretetimesystems |