Structure-preserving discretization for port-Hamiltonian descriptor systems
| dc.contributor.author | Mehrmann, Volker | |
| dc.contributor.author | Morandin, Riccardo | |
| dc.date.accessioned | 2021-12-17T10:16:01Z | |
| dc.date.available | 2021-12-17T10:16:01Z | |
| dc.date.issued | 2019-03-28 | |
| dc.description.abstract | We 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.issn | 2197-8085 | |
| dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/15919 | |
| dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-14692 | |
| dc.language.iso | en | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject.ddc | 510 Mathematik | en |
| dc.subject.other | port-Hamiltonian system | en |
| dc.subject.other | descriptor system | en |
| dc.subject.other | differential-algebraic equation | en |
| dc.subject.other | passivity | en |
| dc.subject.other | stability | en |
| dc.subject.other | system transformation | en |
| dc.subject.other | Dirac structure | en |
| dc.subject.other | geometric numerical integration | en |
| dc.subject.other | symplectic methods | en |
| dc.title | Structure-preserving discretization for port-Hamiltonian descriptor systems | en |
| dc.type | Research Paper | en |
| dc.type.version | submittedVersion | en |
| tub.accessrights.dnb | free | en |
| tub.affiliation | Fak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik | de |
| tub.affiliation.faculty | Fak. 2 Mathematik und Naturwissenschaften | de |
| tub.affiliation.institute | Inst. Mathematik | de |
| tub.publisher.universityorinstitution | Technische Universität Berlin | en |
| tub.series.issuenumber | 2019, 05 | en |
| tub.series.name | Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin | en |
| tub.subject.msc2000 | 65L80 Methods for differential-algebraic equations | en |
| tub.subject.msc2000 | 65P10 Hamiltonian systems including symplectic integrators | en |
| tub.subject.msc2000 | 93D05 Lyapunov and other classical stabilities | en |
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