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    Stability of Nonlinear Stochastic Distributed Parameter Systems and Its Applications

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    Fulltext not available
    Authors
    Do, Khac Duc
    Date
    2016
    Type
    Journal Article
    
    Metadata
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    Citation
    Do, K.D. 2016. Stability of Nonlinear Stochastic Distributed Parameter Systems and Its Applications. Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME. 138 (10): 101010.
    Source Title
    Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME
    DOI
    10.1115/1.4033946
    ISSN
    0022-0434
    School
    Department of Mechanical Engineering
    URI
    http://hdl.handle.net/20.500.11937/51405
    Collection
    • Curtin Research Publications
    Abstract

    This paper derives several well-posedness (existence and uniqueness) and stability results for nonlinear stochastic distributed parameter systems (SDPSs) governed by nonlinear partial differential equations (PDEs) subject to both state-dependent and additive stochastic disturbances. These systems do not need to satisfy global Lipschitz and linear growth conditions. First, the nonlinear SDPSs are transformed to stochastic evolution systems (SESs), which are governed by stochastic ordinary differential equations (SODEs) in appropriate Hilbert spaces, using functional analysis. Second, Lyapunov sufficient conditions are derived to ensure well-posedness and almost sure (a.s.) asymptotic and practical stability of strong solutions. Third, the above results are applied to study well-posedness and stability of the solutions of two exemplary SDPSs.

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