Mehrmann, VolkerMorandin, Riccardo2021-12-172021-12-172019-03-282197-8085https://depositonce.tu-berlin.de/handle/11303/15919http://dx.doi.org/10.14279/depositonce-14692We 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.en510 Mathematikport-Hamiltonian systemdescriptor systemdifferential-algebraic equationpassivitystabilitysystem transformationDirac structuregeometric numerical integrationsymplectic methodsResearch Paper