Uniform exponential stabilization of distributed bilinear parabolic time delay systems with bounded feedback control
In this paper we deal with the problem of uniform exponential stabilization for a class of distributed bilinear parabolic systems with time delay in a Hilbert space by means of a bounded feedback control. The uniform exponential stabilization problem of such a system reduces to stabilizing only its...
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| Format: | Article |
| Language: | English |
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Polish Academy of Sciences
2022-06-01
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| Series: | Archives of Control Sciences |
| Subjects: | |
| Online Access: | https://journals.pan.pl/Content/123553/PDF/art02_int.pdf |
| _version_ | 1811295167270879232 |
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| author | Azzeddine Tsouli Mostafa Ouarit |
| author_facet | Azzeddine Tsouli Mostafa Ouarit |
| author_sort | Azzeddine Tsouli |
| collection | DOAJ |
| description | In this paper we deal with the problem of uniform exponential stabilization for a class of distributed bilinear parabolic systems with time delay in a Hilbert space by means of a bounded feedback control. The uniform exponential stabilization problem of such a system reduces to stabilizing only its projection on a suitable finite dimensional subspace. Furthermore, the stabilizing feedback control depends only on the state projection on the finite dimensional subspace. An explicit decay rate estimate of the stabilized state is given provided that a nonstandard weaker observability condition is satisfied. Illustrative examples for partial functional differential equations are displayed. |
| first_indexed | 2024-04-13T05:28:10Z |
| format | Article |
| id | doaj.art-52f7a092d37b4439b028da2f8a91d690 |
| institution | Directory Open Access Journal |
| issn | 1230-2384 |
| language | English |
| last_indexed | 2024-04-13T05:28:10Z |
| publishDate | 2022-06-01 |
| publisher | Polish Academy of Sciences |
| record_format | Article |
| series | Archives of Control Sciences |
| spelling | doaj.art-52f7a092d37b4439b028da2f8a91d6902022-12-22T03:00:31ZengPolish Academy of SciencesArchives of Control Sciences1230-23842022-06-01vol. 32No 2257278https://doi.org/10.24425/acs.2022.141712Uniform exponential stabilization of distributed bilinear parabolic time delay systems with bounded feedback controlAzzeddine Tsouli0Mostafa Ouarit1Laboratory of Mathematics and Applications, ENSAM, Hassan II University of Casablanca, MoroccoLaboratory of Fundamental and Applied Mathematics LAMFA, Faculty of Sciences Ain Chock, Hassan II University of Casablanca, MoroccoIn this paper we deal with the problem of uniform exponential stabilization for a class of distributed bilinear parabolic systems with time delay in a Hilbert space by means of a bounded feedback control. The uniform exponential stabilization problem of such a system reduces to stabilizing only its projection on a suitable finite dimensional subspace. Furthermore, the stabilizing feedback control depends only on the state projection on the finite dimensional subspace. An explicit decay rate estimate of the stabilized state is given provided that a nonstandard weaker observability condition is satisfied. Illustrative examples for partial functional differential equations are displayed.https://journals.pan.pl/Content/123553/PDF/art02_int.pdftime delayuniform exponential stabilizationbilinear parabolic systemsbounded feedback control |
| spellingShingle | Azzeddine Tsouli Mostafa Ouarit Uniform exponential stabilization of distributed bilinear parabolic time delay systems with bounded feedback control Archives of Control Sciences time delay uniform exponential stabilization bilinear parabolic systems bounded feedback control |
| title | Uniform exponential stabilization of distributed bilinear parabolic time delay systems with bounded feedback control |
| title_full | Uniform exponential stabilization of distributed bilinear parabolic time delay systems with bounded feedback control |
| title_fullStr | Uniform exponential stabilization of distributed bilinear parabolic time delay systems with bounded feedback control |
| title_full_unstemmed | Uniform exponential stabilization of distributed bilinear parabolic time delay systems with bounded feedback control |
| title_short | Uniform exponential stabilization of distributed bilinear parabolic time delay systems with bounded feedback control |
| title_sort | uniform exponential stabilization of distributed bilinear parabolic time delay systems with bounded feedback control |
| topic | time delay uniform exponential stabilization bilinear parabolic systems bounded feedback control |
| url | https://journals.pan.pl/Content/123553/PDF/art02_int.pdf |
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