Necessary and sufficient conditions for stability of impulsive switched linear systems
This paper addresses fundamental stability problems of impulsive switched linear systems, featuring given impulsive switching time intervals and switching rules. First, based on the state dynamical behaviors, we construct a new state transition-like matrix, called an impulsive-type state transition...
| Main Authors: | , , |
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| Format: | Journal Article |
| Published: |
AIMS
2011
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| Online Access: | http://hdl.handle.net/20.500.11937/26874 |
| _version_ | 1848752109575471104 |
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| author | Xu, H. Teo, Kok Lay Gui, W. |
| author_facet | Xu, H. Teo, Kok Lay Gui, W. |
| author_sort | Xu, H. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | This paper addresses fundamental stability problems of impulsive switched linear systems, featuring given impulsive switching time intervals and switching rules. First, based on the state dynamical behaviors, we construct a new state transition-like matrix, called an impulsive-type state transition (IST) matrix. Then, based on the IST matrix and Lyapunov stability theory, necessary and sufficient conditions for the uniform stability, uniform asymptotic stability, and exponential stability of impulsive switched linear systems are established. These stability conditions require the testing on the IST matrix of the impulsive switched linear systems. The results can be reduced to those for switched linear systems without impulsive effects, and also to those for impulsive linear systems without switchings. |
| first_indexed | 2025-11-14T08:03:24Z |
| format | Journal Article |
| id | curtin-20.500.11937-26874 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:03:24Z |
| publishDate | 2011 |
| publisher | AIMS |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-268742017-09-13T16:08:11Z Necessary and sufficient conditions for stability of impulsive switched linear systems Xu, H. Teo, Kok Lay Gui, W. This paper addresses fundamental stability problems of impulsive switched linear systems, featuring given impulsive switching time intervals and switching rules. First, based on the state dynamical behaviors, we construct a new state transition-like matrix, called an impulsive-type state transition (IST) matrix. Then, based on the IST matrix and Lyapunov stability theory, necessary and sufficient conditions for the uniform stability, uniform asymptotic stability, and exponential stability of impulsive switched linear systems are established. These stability conditions require the testing on the IST matrix of the impulsive switched linear systems. The results can be reduced to those for switched linear systems without impulsive effects, and also to those for impulsive linear systems without switchings. 2011 Journal Article http://hdl.handle.net/20.500.11937/26874 10.3934/dcdsb.2011.16.1185 AIMS unknown |
| spellingShingle | Xu, H. Teo, Kok Lay Gui, W. Necessary and sufficient conditions for stability of impulsive switched linear systems |
| title | Necessary and sufficient conditions for stability of impulsive switched linear systems |
| title_full | Necessary and sufficient conditions for stability of impulsive switched linear systems |
| title_fullStr | Necessary and sufficient conditions for stability of impulsive switched linear systems |
| title_full_unstemmed | Necessary and sufficient conditions for stability of impulsive switched linear systems |
| title_short | Necessary and sufficient conditions for stability of impulsive switched linear systems |
| title_sort | necessary and sufficient conditions for stability of impulsive switched linear systems |
| url | http://hdl.handle.net/20.500.11937/26874 |