On the Stability of Tubes of Discontinuous Solutions of Bilinear Systems with Delay
The paper considers the stability property of tubes of discontinuous solutions of a bilinear system with a generalized action on the right-hand side and delay. A feature of the system under consideration is that a generalized (impulsive) effect is possible non-unique reaction of the system. As a res...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Irkutsk State University
2020-03-01
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| Series: | Известия Иркутского государственного университета: Серия "Математика" |
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| Online Access: | http://mathizv.isu.ru/en/article/file?id=1333 |
| _version_ | 1828413255408680960 |
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| author | A.N. Sesekin N. I. Zhelonkina |
| author_facet | A.N. Sesekin N. I. Zhelonkina |
| author_sort | A.N. Sesekin |
| collection | DOAJ |
| description | The paper considers the stability property of tubes of discontinuous solutions of a bilinear system with a generalized action on the right-hand side and delay. A feature of the system under consideration is that a generalized (impulsive) effect is possible non-unique reaction of the system. As a result, the unique generalized action gives rise to a certain set of discontinuous solutions, which in the work will be called the tube of discontinuous solutions.The concept of stability of discontinuous solutions tubes is formalized. Two versions of sufficient conditions for asymptotic stability are obtained. In the first case, the stability of the system is ensured by the stability property of a homogeneous system without delay; in the second case, the stability property is ensured by the stability property of a homogeneous system with delay. These results generalized the similar results for systems without delay. |
| first_indexed | 2024-12-10T13:06:08Z |
| format | Article |
| id | doaj.art-55b809f153be4972bb70fd79cbf3f0f6 |
| institution | Directory Open Access Journal |
| issn | 1997-7670 2541-8785 |
| language | English |
| last_indexed | 2024-12-10T13:06:08Z |
| publishDate | 2020-03-01 |
| publisher | Irkutsk State University |
| record_format | Article |
| series | Известия Иркутского государственного университета: Серия "Математика" |
| spelling | doaj.art-55b809f153be4972bb70fd79cbf3f0f62022-12-22T01:47:51ZengIrkutsk State UniversityИзвестия Иркутского государственного университета: Серия "Математика"1997-76702541-87852020-03-0131196110https://doi.org/10.26516/1997-7670.2020.31.96On the Stability of Tubes of Discontinuous Solutions of Bilinear Systems with DelayA.N. SesekinN. I. ZhelonkinaThe paper considers the stability property of tubes of discontinuous solutions of a bilinear system with a generalized action on the right-hand side and delay. A feature of the system under consideration is that a generalized (impulsive) effect is possible non-unique reaction of the system. As a result, the unique generalized action gives rise to a certain set of discontinuous solutions, which in the work will be called the tube of discontinuous solutions.The concept of stability of discontinuous solutions tubes is formalized. Two versions of sufficient conditions for asymptotic stability are obtained. In the first case, the stability of the system is ensured by the stability property of a homogeneous system without delay; in the second case, the stability property is ensured by the stability property of a homogeneous system with delay. These results generalized the similar results for systems without delay.http://mathizv.isu.ru/en/article/file?id=1333differential equations with delayimpulsive disturbancestability |
| spellingShingle | A.N. Sesekin N. I. Zhelonkina On the Stability of Tubes of Discontinuous Solutions of Bilinear Systems with Delay Известия Иркутского государственного университета: Серия "Математика" differential equations with delay impulsive disturbance stability |
| title | On the Stability of Tubes of Discontinuous Solutions of Bilinear Systems with Delay |
| title_full | On the Stability of Tubes of Discontinuous Solutions of Bilinear Systems with Delay |
| title_fullStr | On the Stability of Tubes of Discontinuous Solutions of Bilinear Systems with Delay |
| title_full_unstemmed | On the Stability of Tubes of Discontinuous Solutions of Bilinear Systems with Delay |
| title_short | On the Stability of Tubes of Discontinuous Solutions of Bilinear Systems with Delay |
| title_sort | on the stability of tubes of discontinuous solutions of bilinear systems with delay |
| topic | differential equations with delay impulsive disturbance stability |
| url | http://mathizv.isu.ru/en/article/file?id=1333 |
| work_keys_str_mv | AT ansesekin onthestabilityoftubesofdiscontinuoussolutionsofbilinearsystemswithdelay AT nizhelonkina onthestabilityoftubesofdiscontinuoussolutionsofbilinearsystemswithdelay |