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Main Title: Structure-preserving discretization for port-Hamiltonian descriptor systems
Author(s): Mehrmann, Volker
Morandin, Riccardo
Type: Research Paper
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.
Subject(s): port-Hamiltonian system
descriptor system
differential-algebraic equation
system transformation
Dirac structure
geometric numerical integration
symplectic methods
Issue Date: 28-Mar-2019
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 65L80 Methods for differential-algebraic equations
65P10 Hamiltonian systems including symplectic integrators
93D05 Lyapunov and other classical stabilities
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2019, 05
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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