Dirac structures and boundary control systems associated with skew-symmetric differential operators

Y. Le Gorrec, Heiko J. Zwart, B.M. Maschke

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    Abstract

    Associated with a skew-symmetric linear operator on the spatial domain $[a,b]$ we define a Dirac structure which includes the port variables on the boundary of this spatial domain. This Dirac structure is a subspace of a Hilbert space. Naturally, associated to this Dirac structure is infinite dimensional system. We parameterize the boundary port variables for which the \( C_{0} \)-semigroup associated to this system is contractive or unitary. Furthermore, this parameterization is used to split the boundary port variables into inputs and outputs. Similarly, we define a linear port controlled Hamiltonian system associated with the previously defined Dirac structure and a symmetric positive operator defining the energy of the system. We illustrate this theory on the example of the Timoshenko Beam.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Publication statusPublished - 2004

    Publication series

    NameMemorandum / Faculty of Mathematical Sciences
    PublisherDepartment of Applied Mathematics, University of Twente
    No.1730
    ISSN (Print)0169-2690

    Keywords

    • MSC-93C25
    • MSC-35M99
    • MSC-70H45
    • IR-65914
    • EWI-3550
    • MSC-47D06
    • MSC-93C20

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