46 citations · 201 across the 50 of their papers we have counts for
65 papers
Canonical forms for pairs of matrices associated with Lagrangian and Dirac subspaces
Sweta Das, Andrii Dmytryshyn, Volker Mehrmann
We derive the canonical forms for a pair of complex matrices under transformations , and , w…
Relationship between dissipativity concepts for linear time-varying port-Hamiltonian systems
Karim Cherifi, Hannes Gernandt, Dorothea Hinsen +2
The relationship between different dissipativity concepts for linear time-varying systems is studied, in particular between port-Hamiltonian systems, passive systems, and systems w…
A geometric framework for discrete time port-Hamiltonian systems
Karim Cherifi, Hannes Gernandt, Dorothea Hinsen +1
Port-Hamiltonian systems provide an energy-based formulation with a model class that is closed under structure preserving interconnection. For continuous-time systems these interco…
Hypocoercivity in Hilbert spaces
Franz Achleitner, Anton Arnold, Volker Mehrmann +1
The concept of hypocoercivity for linear evolution equations with dissipation is discussed and equivalent characterizations that were developed for the finite-dimensional case are…
Hidden regularity in singular optimal control of port-Hamiltonian systems
Timm Faulwasser, Jonas Kirchhoff, Volker Mehrmann +3
We study the problem of state transition on a finite time interval with minimal energy supply for linear port-Hamiltonian systems. While the cost functional of minimal energy suppl…
On discrete-time dissipative port-Hamiltonian (descriptor) systems
Karim Cherifi, Hannes Gernandt, Dorothea Hinsen +1
Port-Hamiltonian (pH) systems have been studied extensively for linear continuous-time dynamical systems. This manuscript presents a discrete-time pH descriptor formulation for lin…
Hypocoercivity in algebraically constrained partial differential equations with application to Oseen equations
Franz Achleitner, Anton Arnold, Volker Mehrmann
The long-time behavior of solutions to different versions of Oseen equations of fluid flow on the 2D torus is analyzed using the concept of hypocoercivity. The considered models ar…
Fiedler Linearizations of Rectangular Rational Matrix Functions
Namita Behera, Avisek Bist, Volker Mehrmann
Linearization is a standard approach in the computation of eigenvalues, eigenvectors and invariant subspaces of matrix polynomials and rational matrix value functions. An important…
Linear port-Hamiltonian DAE systems revisited
Arjan van der Schaft, Volker Mehrmann
Port-Hamiltonian systems theory provides a systematic methodology for the modeling, simulation and control of multi-physics systems. The incorporation of algebraic constraints has…
Differential-algebraic systems with dissipative Hamiltonian structure
V. Mehrmann, A. J. van der Schaft
Different representations of dissipative Hamiltonian and port-Hamiltonian differential-algebraic equations (DAE) systems are presented and compared. Using global geometric and alge…
Hierarchical modeling for an industrial implementation of a Digital Twin for electrical drives
Karim Cherifi, Philipp Schulze, Volker Mehrmann +2
Digital twins have become popular for their ability to monitor and optimize a process or a machine, ideally through its complete life cycle using simulations and sensor data. In th…
Structure-Preserving Model Order Reduction for Index Two Port-Hamiltonian Descriptor Systems
Tim Moser, Paul Schwerdtner, Volker Mehrmann +1
We present a new optimization-based structure-preserving model order reduction (MOR) method for port-Hamiltonian descriptor systems (pH-DAEs) with differentiation index two. Our me…
Structure-Preserving Model Order Reduction for Index One Port-Hamiltonian Descriptor Systems
Paul Schwerdtner, Tim Moser, Volker Mehrmann +1
We develop optimization-based structure-preserving model order reduction (MOR) methods for port-Hamiltonian (pH) descriptor systems of differentiation index one. Descriptor systems…
Discretization of inherent ODEs and the geometric integration of DAEs with symmetries
Peter Kunkel, Volker Mehrmann
Discretization methods for differential-algebraic equations (DAEs) are considered that are based on the integration of an associated inherent ordinary differential equation (ODE).…
Hypocoercivity and hypocontractivity concepts for linear dynamical systems
Franz Achleitner, Anton Arnold, Volker Mehrmann
For linear dynamical systems (in continuous-time and discrete-time) we revisit and extend the concepts of hypocoercivity and hypocontractivity and give a detailed analysis of the r…
A Lagrange subspace approach to dissipation inequalities
Arjan van der Schaft, Volker Mehrmann
The standard dissipation inequality for passivity is extended from storage functions to general Lagrange subspaces. This is shown to have some interesting consequences. A classical…
Local and global canonical forms for differential-algebraic equations with symmetries
Peter Kunkel, Volker Mehrmann
Linear time-varying differential-algebraic equations with symmetries are studied. The structures that we address are self-adjoint and skew-adjoint systems. Local and global canonic…
Adaptive Nonlinear Optimization of District Heating Networks Based on Model and Discretization Catalogs
Hannes Dänschel, Volker Mehrmann, Marius Roland +1
We propose an adaptive optimization algorithm for operating district heating networks in a stationary regime. The behavior of hot water flow in the pipe network is modeled using th…
Port-Hamiltonian Realizations of Nonminimal Linear Time Invariant Systems
Christopher Beattie, Volker Mehrmann, Hongguo Xu
Numerical methods for developing port-Hamiltonian representations of general linear time-invariant systems are studied. The approach extends previous port-Hamiltonian characterizat…
On non-Hermitian positive (semi)definite linear algebraic systems arising from dissipative Hamiltonian DAEs
Candan Güdücü, Jörg Liesen, Volker Mehrmann +1
We discuss different cases of dissipative Hamiltonian differential-algebraic equations and the linear algebraic systems that arise in their linearization or discretization. For eac…
Error Analysis of a Model Order Reduction Framework for Financial Risk Analysis
Andreas Binder, Onkar Jadhav, Volker Mehrmann
A parametric model order reduction (MOR) approach for simulating the high dimensional models arising in financial risk analysis is proposed on the basis of the proper orthogonal de…
Computation of the nearest structured matrix triplet with common null space
Nicola Guglielmi, Volker Mehrmann
We study computational methods for computing the distance to singularity, the distance to the nearest high index problem, and the distance to instability for linear differential-al…
Matrix pencils with coefficients that have positive semidefinite Hermitian part
Christian Mehl, Volker Mehrmann, Michal Wojtylak
We analyze when an arbitrary matrix pencil is equivalent to a dissipative Hamiltonian pencil and show that this heavily restricts the spectral properties. In order to relax the spe…
Hypocoercivity and controllability in linear semi-dissipative Hamiltonian ODEs and DAEs
Franz Achleitner, Anton Arnold, Volker Mehrmann
For the classes of finite dimensional linear time-invariant semi-dissipative Hamiltonian ordinary differential equations and differential-algebraic equations, stability and hypocoe…