A semigroup approach to Port Hamiltonian systems associated with linear skew symmetric operator

Y. Le Gorrec, H. Zwart, B. Maschke

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    Abstract

    In this paper we first define a Dirac structure on a Hilbert spaces associated with a skew-symmetric linear operator including port variables on the boundary of its domain. Secondly, we associate $C_0$-semigroup with some parameterization of the boundary port variables and define a family of boundary control systems. Thirdly we define a linear port controlled Hamiltonian system associated with the previously defined Dirac structure and generated by a symmetric positive operator defining the energy of the system.
    Original languageEnglish
    Title of host publicationProceedings 16th International symposium on Mathematical Theory of Networks and Systems
    Subtitle of host publicationLeuven, Belgium, July 5-9, 2004
    EditorsBart De Mor, Bart Motmans, Jan Willems, Paul Van Dooren, Vincent Blondel
    Place of PublicationLeuven, Belgium
    PublisherKatholieke Universiteit Leuven
    Number of pages14
    ISBN (Print)90-5682-517-8
    Publication statusPublished - 2004
    Event16th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2004 - Leuven, Belgium
    Duration: 5 Jul 20049 Jul 2004
    Conference number: 16

    Conference

    Conference16th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2004
    Abbreviated titleMTNS
    CountryBelgium
    CityLeuven
    Period5/07/049/07/04

    Keywords

    • MSC-93C20

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  • Cite this

    Le Gorrec, Y., Zwart, H., & Maschke, B. (2004). A semigroup approach to Port Hamiltonian systems associated with linear skew symmetric operator. In B. De Mor, B. Motmans, J. Willems, P. Van Dooren, & V. Blondel (Eds.), Proceedings 16th International symposium on Mathematical Theory of Networks and Systems: Leuven, Belgium, July 5-9, 2004 Leuven, Belgium: Katholieke Universiteit Leuven.