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Article: KL*-stability for a class of hybrid dynamical systems
Title | KL*-stability for a class of hybrid dynamical systems |
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Authors | |
Keywords | Dwell-Time Hybrid dynamical system KL-stability Stability |
Issue Date | 2017 |
Publisher | Oxford University Press. The Journal's web site is located at http://imamat.oxfordjournals.org/ |
Citation | IMA Journal of Applied Mathematics, 2017, v. 82 n. 5, p. 1043-1060 How to Cite? |
Abstract | 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. |
Persistent Identifier | http://hdl.handle.net/10722/264130 |
ISSN | 2023 Impact Factor: 1.4 2023 SCImago Journal Rankings: 0.389 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Liu, B | - |
dc.contributor.author | Dam, HHH | - |
dc.contributor.author | Teo, KL | - |
dc.contributor.author | Hill, DJ | - |
dc.date.accessioned | 2018-10-22T07:50:03Z | - |
dc.date.available | 2018-10-22T07:50:03Z | - |
dc.date.issued | 2017 | - |
dc.identifier.citation | IMA Journal of Applied Mathematics, 2017, v. 82 n. 5, p. 1043-1060 | - |
dc.identifier.issn | 0272-4960 | - |
dc.identifier.uri | http://hdl.handle.net/10722/264130 | - |
dc.description.abstract | 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. | - |
dc.language | eng | - |
dc.publisher | Oxford University Press. The Journal's web site is located at http://imamat.oxfordjournals.org/ | - |
dc.relation.ispartof | IMA Journal of Applied Mathematics | - |
dc.rights | Pre-print: Journal Title] ©: [year] [owner as specified on the article] Published by Oxford University Press [on behalf of xxxxxx]. All rights reserved. Pre-print (Once an article is published, preprint notice should be amended to): This is an electronic version of an article published in [include the complete citation information for the final version of the Article as published in the print edition of the Journal.] Post-print: This is a pre-copy-editing, author-produced PDF of an article accepted for publication in [insert journal title] following peer review. The definitive publisher-authenticated version [insert complete citation information here] is available online at: xxxxxxx [insert URL that the author will receive upon publication here]. | - |
dc.subject | Dwell-Time | - |
dc.subject | Hybrid dynamical system | - |
dc.subject | KL-stability | - |
dc.subject | Stability | - |
dc.title | KL*-stability for a class of hybrid dynamical systems | - |
dc.type | Article | - |
dc.identifier.email | Hill, DJ: dhill@eee.hku.hk | - |
dc.identifier.authority | Hill, DJ=rp01669 | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1093/imamat/hxx023 | - |
dc.identifier.scopus | eid_2-s2.0-85036460078 | - |
dc.identifier.hkuros | 293569 | - |
dc.identifier.volume | 82 | - |
dc.identifier.issue | 5 | - |
dc.identifier.spage | 1043 | - |
dc.identifier.epage | 1060 | - |
dc.identifier.isi | WOS:000412767300005 | - |
dc.publisher.place | United Kingdom | - |
dc.identifier.issnl | 0272-4960 | - |