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    KL-stability for a class of hybrid dynamical systems

    Access Status
    Open access via publisher
    Authors
    Liu, B.
    Dam, H.
    Teo, Kok Lay
    Hill, D.
    Date
    2017
    Type
    Journal Article
    
    Metadata
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    Citation
    Liu, B. and Dam, H. and Teo, K.L. and Hill, D. 2017. KL-stability for a class of hybrid dynamical systems. IMA Journal of Applied Mathematics. 82 (5): pp. 1043-1060.
    Source Title
    IMA Journal of Applied Mathematics
    DOI
    10.1093/imamat/hxx023
    ISSN
    0272-4960
    School
    School of Electrical Engineering, Computing and Mathematical Science (EECMS)
    URI
    http://hdl.handle.net/20.500.11937/61331
    Collection
    • Curtin Research Publications
    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.

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