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Structure-preserving discretization for port-Hamiltonian descriptor systems

  • 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.

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Metadaten
Author:Volker Mehrmann, Riccardo Morandin
Document Type:Preprint
Language:English
Date of Publication (online):2019/03/25
Date of first Publication:2021/07/13
Release Date:2021/07/13
Tag:Dirac structure; differential-algebraic equations; port-Hamiltonian systems; structure-preserving discretization
Institutes:Technische Universität Berlin
Subprojects:B03
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International