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  <doc>
    <id>465</id>
    <completedYear>2021</completedYear>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>preprint</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>2021-11-05</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Structure-Preserving Linear Quadratic Gaussian Balanced Truncation for Port-Hamiltonian Descriptor Systems</title>
    <abstract language="eng">We present a new balancing-based structure-preserving model reduc-&#13;
tion technique for linear port-Hamiltonian descriptor systems. The pro-&#13;
posed method relies on a modification of a set of two dual generalized&#13;
algebraic Riccati equations that arise in the context of linear quadratic&#13;
Gaussian balanced truncation for differential algebraic systems. We de-&#13;
rive an a priori error bound with respect to a right coprime factorization&#13;
of the underlying transfer function thereby allowing for an estimate with&#13;
respect to the gap metric. We further theoretically and numerically ana-&#13;
lyze the influence of the Hamiltonian and a change thereof, respectively.&#13;
With regard to this change of the Hamiltonian, we provide a novel proce-&#13;
dure that is based on a recently introduced Kalman–Yakubovich–Popov&#13;
inequality for descriptor systems. Numerical examples demonstrate how&#13;
the quality of reduced-order models can significantly be improved by first&#13;
computing an extremal solution to this inequality.</abstract>
    <enrichment key="opus.source">publish</enrichment>
    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <author>Tobias Breiten</author>
    <author>Philipp Schulze</author>
    <collection role="institutes" number="">Technische Universität Berlin</collection>
    <collection role="subprojects" number="">B03</collection>
    <file>https://opus4.kobv.de/opus4-trr154/files/465/main.pdf</file>
  </doc>
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