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Structure-Preserving Interpolatory Model Reduction for Port-Hamiltonian Differential-Algebraic Systems

In: Realization and Model Reduction of Dynamical Systems

Author

Listed:
  • Christopher Beattie

    (Virginia Tech, Department of Mathematics)

  • Serkan Gugercin

    (Virginia Tech, Department of Mathematics)

  • Volker Mehrmann

    (Institut für Mathematik, MA 4-5, Technische Universität Berlin)

Abstract

We examine interpolatory model reduction methods that are particularly well-suited for treating large-scale port-Hamiltonian differential-algebraic systems. We are able to take advantage of underlying structural features of the system in a way that preserves them in the reduced model, using approaches that incorporate regularization and a prudent selection of interpolation data. We focus on linear time-invariant systems and present a systematic treatment of a variety of model classes that include combinations of index-1 and index-2 systems, describing in particular how constraints may be represented in the transfer function so that the polynomial part can be preserved with interpolatory methods. We propose an algorithm to generate effective interpolatory models and illustrate its effectiveness on a numerical example.

Suggested Citation

  • Christopher Beattie & Serkan Gugercin & Volker Mehrmann, 2022. "Structure-Preserving Interpolatory Model Reduction for Port-Hamiltonian Differential-Algebraic Systems," Springer Books, in: Christopher Beattie & Peter Benner & Mark Embree & Serkan Gugercin & Sanda Lefteriu (ed.), Realization and Model Reduction of Dynamical Systems, pages 235-254, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-95157-3_13
    DOI: 10.1007/978-3-030-95157-3_13
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