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...

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Main Authors: Liu, B., Dam, H., Teo, Kok Lay, Hill, D.
Format: Journal Article
Published: Oxford University Press 2017
Online Access:http://hdl.handle.net/20.500.11937/61331
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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.
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publishDate 2017
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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