Robust finite-time stability of nonlinear systems involving hybrid impulses with application to sliding-mode control
This paper is concerned with the robust finite-time stability and stabilization of impulsive systems subject to hybrid disturbances that consists of external disturbances and hybrid impulses with time-varying jump maps. First, the global finite-time stability and local finite-time stability of a sca...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-01-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2023196?viewType=HTML |
| _version_ | 1797938819506372608 |
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| author | Jian Meng Bin Zhang Tengda Wei Xinyi He Xiaodi Li |
| author_facet | Jian Meng Bin Zhang Tengda Wei Xinyi He Xiaodi Li |
| author_sort | Jian Meng |
| collection | DOAJ |
| description | This paper is concerned with the robust finite-time stability and stabilization of impulsive systems subject to hybrid disturbances that consists of external disturbances and hybrid impulses with time-varying jump maps. First, the global finite-time stability and local finite-time stability of a scalar impulsive system are ensured by the analysis of cumulative effect of hybrid impulses. Then, asymptotic stabilization and finite-time stabilization of second-order system subject to hybrid disturbances are achieved by linear sliding-mode control and non-singular terminal sliding-mode control. It shows that the stable systems under control are robust to external disturbances and hybrid impulses with non-destabilizing cumulative effect. If the hybrid impulses have destabilizing cumulative effect, the systems are also capable of absorbing the hybrid impulsive disturbances by the designed sliding-mode control strategies. Finally, the effectiveness of theoretical results is verified by numerical simulation and the tracking control of linear motor. |
| first_indexed | 2024-04-10T19:05:40Z |
| format | Article |
| id | doaj.art-7f691e7f77cb4afe9aaa83ae37c77548 |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-04-10T19:05:40Z |
| publishDate | 2023-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-7f691e7f77cb4afe9aaa83ae37c775482023-01-31T02:40:09ZengAIMS PressMathematical Biosciences and Engineering1551-00182023-01-012024198421810.3934/mbe.2023196Robust finite-time stability of nonlinear systems involving hybrid impulses with application to sliding-mode controlJian Meng 0Bin Zhang 1Tengda Wei2Xinyi He3Xiaodi Li 41. State Grid Intelligence Technology Co., Ltd, Jinan 250000, China 2. School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China1. State Grid Intelligence Technology Co., Ltd, Jinan 250000, China2. School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China2. School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China2. School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, ChinaThis paper is concerned with the robust finite-time stability and stabilization of impulsive systems subject to hybrid disturbances that consists of external disturbances and hybrid impulses with time-varying jump maps. First, the global finite-time stability and local finite-time stability of a scalar impulsive system are ensured by the analysis of cumulative effect of hybrid impulses. Then, asymptotic stabilization and finite-time stabilization of second-order system subject to hybrid disturbances are achieved by linear sliding-mode control and non-singular terminal sliding-mode control. It shows that the stable systems under control are robust to external disturbances and hybrid impulses with non-destabilizing cumulative effect. If the hybrid impulses have destabilizing cumulative effect, the systems are also capable of absorbing the hybrid impulsive disturbances by the designed sliding-mode control strategies. Finally, the effectiveness of theoretical results is verified by numerical simulation and the tracking control of linear motor.https://www.aimspress.com/article/doi/10.3934/mbe.2023196?viewType=HTMLrobust finite-time stabilityhybrid impulsesliding-mode controlsecond-order dynamics |
| spellingShingle | Jian Meng Bin Zhang Tengda Wei Xinyi He Xiaodi Li Robust finite-time stability of nonlinear systems involving hybrid impulses with application to sliding-mode control Mathematical Biosciences and Engineering robust finite-time stability hybrid impulse sliding-mode control second-order dynamics |
| title | Robust finite-time stability of nonlinear systems involving hybrid impulses with application to sliding-mode control |
| title_full | Robust finite-time stability of nonlinear systems involving hybrid impulses with application to sliding-mode control |
| title_fullStr | Robust finite-time stability of nonlinear systems involving hybrid impulses with application to sliding-mode control |
| title_full_unstemmed | Robust finite-time stability of nonlinear systems involving hybrid impulses with application to sliding-mode control |
| title_short | Robust finite-time stability of nonlinear systems involving hybrid impulses with application to sliding-mode control |
| title_sort | robust finite time stability of nonlinear systems involving hybrid impulses with application to sliding mode control |
| topic | robust finite-time stability hybrid impulse sliding-mode control second-order dynamics |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2023196?viewType=HTML |
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