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    Necessary and sufficient conditions for stability of impulsive switched linear systems

    Access Status
    Open access via publisher
    Authors
    Xu, H.
    Teo, Kok Lay
    Gui, W.
    Date
    2011
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Xu, Honglei and Teo, Kok Lay and Gui, Weihua. 2011. Necessary and sufficient conditions for stability of impulsive switched linear systems. Discrete and Continuous Dynamical Systems B. 16 (4): pp. 1185-1195.
    Source Title
    Discrete and Continuous Dynamical Systems B
    DOI
    10.3934/dcdsb.2011.16.1185
    ISSN
    15313492
    School
    Department of Mathematics and Statistics
    URI
    http://hdl.handle.net/20.500.11937/26874
    Collection
    • Curtin Research Publications
    Abstract

    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.

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