KL-stability for a class of hybrid dynamical systems
This article studies KL-stability (the stability expressed by KL-class function) for a class of hybrid dynamical systems (HDS). The notions ofKLK-property andKL-stability are proposed for HDS with respect to the hybrid-event-Time. The KL-stability, which is based on K or L property of the continuous...
| Main Authors: | , , , |
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| Format: | Journal Article |
| Published: |
Oxford University Press
2017
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| Online Access: | http://hdl.handle.net/20.500.11937/61331 |
| _version_ | 1848760680394522624 |
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| author | Liu, B. Dam, H. Teo, Kok Lay Hill, D. |
| author_facet | Liu, B. Dam, H. Teo, Kok Lay Hill, D. |
| author_sort | Liu, B. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | This article studies KL-stability (the stability expressed by KL-class function) for a class of hybrid dynamical systems (HDS). The notions ofKLK-property andKL-stability are proposed for HDS with respect to the hybrid-event-Time. The KL-stability, which is based on K or L property of the continuous flow, the discrete jump, and the event in an HDS, extends theKLL-stability and the event-stability reported in the literature for HDS. The relationships between KLK-property and KL-stability are established via introducing the hybrid dwell-Time condition (HDT). The HDT generalizes the average dwell-Time condition in the literature. For an HDS with KLK-property consisting of stabilizing L-property and destabilizing K-property, it is shown that there exists a common HDT under which the HDS will achieve KL-stability. Thus HDT may help to derive some easily tested conditions for HDS to achieve uniform asymptotic stability. Moreover, a criterion ofKL-stability is derived by using the multiple Lyapunov-like functions. Examples are given to illustrate the obtained theoretical results. |
| first_indexed | 2025-11-14T10:19:37Z |
| format | Journal Article |
| id | curtin-20.500.11937-61331 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:19:37Z |
| publishDate | 2017 |
| publisher | Oxford University Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-613312018-05-22T01:42:31Z KL-stability for a class of hybrid dynamical systems Liu, B. Dam, H. Teo, Kok Lay Hill, D. This article studies KL-stability (the stability expressed by KL-class function) for a class of hybrid dynamical systems (HDS). The notions ofKLK-property andKL-stability are proposed for HDS with respect to the hybrid-event-Time. The KL-stability, which is based on K or L property of the continuous flow, the discrete jump, and the event in an HDS, extends theKLL-stability and the event-stability reported in the literature for HDS. The relationships between KLK-property and KL-stability are established via introducing the hybrid dwell-Time condition (HDT). The HDT generalizes the average dwell-Time condition in the literature. For an HDS with KLK-property consisting of stabilizing L-property and destabilizing K-property, it is shown that there exists a common HDT under which the HDS will achieve KL-stability. Thus HDT may help to derive some easily tested conditions for HDS to achieve uniform asymptotic stability. Moreover, a criterion ofKL-stability is derived by using the multiple Lyapunov-like functions. Examples are given to illustrate the obtained theoretical results. 2017 Journal Article http://hdl.handle.net/20.500.11937/61331 10.1093/imamat/hxx023 Oxford University Press unknown |
| spellingShingle | Liu, B. Dam, H. Teo, Kok Lay Hill, D. KL-stability for a class of hybrid dynamical systems |
| title | KL-stability for a class of hybrid dynamical systems |
| title_full | KL-stability for a class of hybrid dynamical systems |
| title_fullStr | KL-stability for a class of hybrid dynamical systems |
| title_full_unstemmed | KL-stability for a class of hybrid dynamical systems |
| title_short | KL-stability for a class of hybrid dynamical systems |
| title_sort | kl-stability for a class of hybrid dynamical systems |
| url | http://hdl.handle.net/20.500.11937/61331 |