Structure-preserving discretization for port-Hamiltonian descriptor systems

dc.contributor.authorMehrmann, Volker
dc.contributor.authorMorandin, Riccardo
dc.date.accessioned2021-12-17T10:16:01Z
dc.date.available2021-12-17T10:16:01Z
dc.date.issued2019-03-28
dc.description.abstractWe extend the modeling framework of port-Hamiltonian descriptor systems to include under- and over-determined systems and arbitrary differentiable Hamiltonian functions. This structure is associated with a Dirac structure that encloses its energy balance properties. In particular, port-Hamiltonian systems are naturally passive and Lyapunov stable, because the Hamiltonian defines a Lyapunov function. The explicit representation of input and dissipation in the structure make these systems particularly suitable for output feedback control. It is shown that this structure is invariant under a wide class of nonlinear transformations, and that it can be naturally modularized, making it adequate for automated modeling. We investigate then the application of time-discretization schemes to these systems and we show that, under certain assumptions on the Hamiltonian, structure preservation is achieved for some methods. Numerical examples are provided.en
dc.identifier.issn2197-8085
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/15919
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-14692
dc.language.isoenen
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.ddc510 Mathematiken
dc.subject.otherport-Hamiltonian systemen
dc.subject.otherdescriptor systemen
dc.subject.otherdifferential-algebraic equationen
dc.subject.otherpassivityen
dc.subject.otherstabilityen
dc.subject.othersystem transformationen
dc.subject.otherDirac structureen
dc.subject.othergeometric numerical integrationen
dc.subject.othersymplectic methodsen
dc.titleStructure-preserving discretization for port-Hamiltonian descriptor systemsen
dc.typeResearch Paperen
dc.type.versionsubmittedVersionen
tub.accessrights.dnbfreeen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften>Inst. Mathematikde
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen
tub.series.issuenumber2019, 05en
tub.series.namePreprint-Reihe des Instituts für Mathematik, Technische Universität Berlinen
tub.subject.msc200065L80 Methods for differential-algebraic equationsen
tub.subject.msc200065P10 Hamiltonian systems including symplectic integratorsen
tub.subject.msc200093D05 Lyapunov and other classical stabilitiesen
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