Dissipative linear stochastic hamiltonian systems

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    Abstract

    This paper is concerned with stochastic Hamiltonian systems which model a class of open dynamical systems subject to random external forces. Their dynamics are governed by Ito stochastic differential equations whose structure is specified by a Hamiltonian, viscous damping parameters and system-environment coupling functions. We consider energy balance relations for such systems with an emphasis on linear stochastic Hamiltonian (LSH) systems with quadratic Hamiltonians and linear coupling. For LSH systems, we also discuss stability conditions, the structure of the invariant measure and its relation with stochastic versions of the virial theorem. Using Lyapunov functions, organised as deformed Hamiltonians, dissipation relations are also considered for LSH systems driven by statistically uncertain external forces. An application of these results to feedback connections of LSH systems is outlined.

    Original languageEnglish
    Title of host publicationANZCC 2018 - 2018 Australian and New Zealand Control Conference
    PublisherInstitute of Electrical and Electronics Engineers Inc.
    Pages227-232
    Number of pages6
    ISBN (Electronic)9781538666173
    DOIs
    Publication statusPublished - 2 Jul 2018
    Event2018 Australian and New Zealand Control Conference, ANZCC 2018 - Melbourne, Australia
    Duration: 7 Dec 20188 Dec 2018

    Publication series

    NameANZCC 2018 - 2018 Australian and New Zealand Control Conference

    Conference

    Conference2018 Australian and New Zealand Control Conference, ANZCC 2018
    Country/TerritoryAustralia
    CityMelbourne
    Period7/12/188/12/18

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