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

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

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    144 Citations (Scopus)
    107 Downloads (Pure)

    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 with this Dirac structure is an infinite-dimensional system. We parameterize the boundary port variables for which the $C_{0}$-semigroup associated with 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 languageEnglish
    Pages (from-to)1864-1892
    Number of pages28
    JournalSIAM journal on control and optimization
    Volume44
    Issue number5
    DOIs
    Publication statusPublished - Dec 2005

    Keywords

    • Port Hamiltonian systems
    • Strongly continuous semigroup
    • Boundary control systems (BCS)
    • Dirac structures

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