Linear port-Hamiltonian descriptor systems

Christopher Beattie, Volker Mehrmann* (Corresponding Author), Hongguo Xu, Hans Zwart

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

    35 Citations (Scopus)
    170 Downloads (Pure)

    Abstract

    The modeling framework of port-Hamiltonian systems is systematically extended to linear constrained dynamical systems (descriptor systems, differential-algebraic equations) of arbitrary index and with time-varying constraints. A new algebraically and geometrically defined system structure is derived. It is shown that this structure is invariant under equivalence transformations, and that it is adequate also for the modeling of high-index descriptor systems. The regularization procedure for descriptor systems to make them suitable for simulation and control is modified to preserve the port-Hamiltonian form. The relevance of the new structure is demonstrated with several examples.

    Original languageEnglish
    Article number17
    Number of pages27
    JournalMathematics of Control, Signals, and Systems
    Volume30
    Issue number4
    DOIs
    Publication statusPublished - 1 Dec 2018

    Keywords

    • UT-Hybrid-D
    • Differential-algebraic equation
    • Differentiation index
    • Passivity
    • Port-Hamiltonian system
    • Skew-adjoint operator
    • Stability
    • Strangeness-index
    • System transformation
    • Descriptor system

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