Prof. Dr Matthias Voigt

Publications

2024

• Model Reduction of Parametric Differential-Algebraic Systems by Balanced Truncation
  Jennifer Przybilla, Matthias Voigt
  Mathematical and Computer Modelling of Dynamical Systems. https://doi.org/10.1080/13873954.2024.2328662
• Structure-Preserving Model Reduction for Dissipative Mechanical Systems
  Rebekka S. Beddig, Peter Benner, Ines Dorschky, Timo Reis, Paul Schwerdtner, Matthias Voigt, Steffen W. R. Werner
  Calm, Smooth and Smart. https://doi.org/10.1007/978-3-031-36143-2_11
• Structure-Preserving Model Reduction of Port-Hamiltonian Systems by Optimization
  Paul Schwerdtner, Matthias Voigt
  26th International Symposium on Mathematical Theory of Networks and Systems

2023

• Balanced truncation model reduction with a priori error bounds for LTI systems with nonzero initial value
  Christian Schröder, Matthias Voigt
  Journal of Computational and Applied Mathematics. https://doi.org/10.1016/j.cam.2022.114708
• Fixed-order H-infinity controller design for port-Hamiltonian systems
  Paul Schwerdtner, Matthias Voigt
  Automatica. https://doi.org/10.1016/j.automatica.2023.110918
• Optimization-based model order reduction of port-Hamiltonian descriptor systems
  Paul Schwerdtner, Tim Moser, Volker Mehrmann, Matthias Voigt
  Systems & Control Letters. https://doi.org/10.1016/j.sysconle.2023.105655
• SOBMOR: Structured Optimization-Based Model Order Reduction
  Paul Schwerdtner, Matthias Voigt
  SIAM Journal on Scientific Computing. https://doi.org/10.1137/20M1380235

2022

• Derivative Interpolating Subspace Frameworks for Nonlinear Eigenvalue Problems
  Rifqi Aziz, Emre Mengi, Matthias Voigt
  SIAM Journal on Scientific Computing. https://doi.org/10.1137/20m1348455
• Discounted cost linear quadratic Gaussian control for descriptor systems
  Hermann Mena, Lena-Maria Pfurtscheller, Matthias Voigt
  International Journal of Control. https://doi.org/10.1080/00207179.2020.1854865
• Optimization-based structured reduced order modeling from frequency samples
  Paul Schwerdtner, Matthias Voigt
  MATHMOD 2022 Discussion Contribution Volume. https://doi.org/10.11128/arep.17

2021

• A greedy reduced basis algorithm for structural acoustic systems with parameter and implicit frequency dependence
  Christopher Jelich, Suhaib Koji Baydoun, Matthias Voigt, Steffen Marburg
  International Journal for Numerical Methods in Engineering. https://doi.org/10.1002/nme.6835
• A subspace iteration eigensolver based on Cauchy integrals for vibroacoustic problems in unbounded domains
  Suhaib Koji Baydoun, Matthias Voigt, Benedikt Goderbauer, Christopher Jelich, Steffen Marburg
  International Journal for Numerical Methods in Engineering. https://doi.org/10.1002/nme.6701
• Adaptive Sampling for Structure-Preserving Model Order Reduction of Port-Hamiltonian Systems
  Paul Schwerdtner, Matthias Voigt
  IFAC-PapersOnLine. https://doi.org/10.1016/j.ifacol.2021.11.069
• Balanced Truncation Model Reduction for Symmetric Second Order Systems---A Passivity-Based Approach
  Ines Dorschky, Timo Reis, Matthias Voigt
  SIAM Journal on Matrix Analysis and Applications. https://doi.org/10.1137/20m1346109
• Low-Rank Iteration Schemes for the Multi-Frequency Solution of Acoustic Boundary Element Equations
  Suhaib Koji Baydoun, Matthias Voigt, Steffen Marburg
  Journal of Theoretical and Computational Acoustics. https://doi.org/10.1142/s2591728521500043

2020

• A greedy reduced basis scheme for multifrequency solution of structural acoustic systems
  Suhaib Koji Baydoun, Matthias Voigt, Christopher Jelich, Steffen Marburg
  International Journal for Numerical Methods in Engineering. https://doi.org/10.1002/nme.6205
• A Subspace Framework for ℋ∞-Norm Minimization
  Nicat Aliyev, Peter Benner, Emre Mengi, Matthias Voigt
  SIAM Journal on Matrix Analysis and Applications. https://doi.org/10.1137/19m125892x
• Certifying Global Optimality for the L∞-Norm Computation of Large-Scale Descriptor Systems
  P. Schwerdtner, E. Mengi, M. Voigt
  IFAC-PapersOnLine. https://doi.org/10.1016/j.ifacol.2020.12.2482
• Semi‐active ℋ∞ damping optimization by adaptive interpolation
  Zoran Tomljanović, Matthias Voigt
  Numerical Linear Algebra with Applications. https://doi.org/10.1002/nla.2300

2019

• Linear-Quadratic Optimal Control of Differential-Algebraic Systems: The Infinite Time Horizon Problem with Zero Terminal State
  Timo Reis, Matthias Voigt
  SIAM Journal on Control and Optimization. https://doi.org/10.1137/18m1189609
• Model Reduction for Second‐Order Dynamical Systems Revisited
  Rebekka S. Beddig, Peter Benner, Ines Dorschky, Timo Reis, Paul Schwerdtner, Matthias Voigt, Steffen W. R. Werner
  Pamm. https://doi.org/10.1002/pamm.201900224
• On linear-quadratic optimal control of implicit difference equations
  Daniel Bankmann, Matthias Voigt
  IMA Journal of Mathematical Control and Information. https://doi.org/10.1093/imamci/dny007

2018

• A Low-Rank Iteration Scheme for Multi-Frequency Acoustic Problems 
  Suhaib Baydoun, Lei Li, Matthias Voigt, Steffen Marburg
  INTER-NOISE and NOISE-CON Congress and Conference Proceedings
• Computation of the L∞-Norm Using Rational Interpolation
  P. Schwerdtner, M. Voigt
  IFAC-PapersOnLine. https://doi.org/10.1016/j.ifacol.2018.11.086
• Inner–outer factorization for differential-algebraic systems
  Timo Reis, Matthias Voigt
  Mathematics of Control, Signals, and Systems. https://doi.org/10.1007/s00498-018-0221-5
• Model reduction of constrained mechanical systems in M-M.E.S.S.
  Jens Saak, Matthias Voigt
  IFAC-PapersOnLine. https://doi.org/10.1016/j.ifacol.2018.03.112
• ℒ∞-norm computation for large-scale descriptor systems using structured iterative eigensolvers
  Peter Benner, Ryan Lowe, Matthias Voigt
  Numerical Algebra, Control & Optimization. https://doi.org/10.3934/naco.2018007

2017

• A Greedy Subspace Method for Computing the ℒ∞-Norm
  Nicat Aliyev, Peter Benner, Emre Mengi, Paul Schwerdtner, Matthias Voigt
  Pamm. https://doi.org/10.1002/pamm.201710343
• Large-Scale Computation of ℒ∞-Norms by a Greedy Subspace Method
  Nicat Aliyev, Peter Benner, Emre Mengi, Paul Schwerdtner, Matthias Voigt
  SIAM Journal on Matrix Analysis and Applications. https://doi.org/10.1137/16m1086200

2016

• Algorithm 961: Fortran 77 Subroutines for the Solution of Skew-Hamiltonian/Hamiltonian Eigenproblems
  Peter Benner, Vasile Sima, Matthias Voigt
  ACM Transactions on Mathematical Software. https://doi.org/10.1145/2818313
• Inner-Outer Factorization via Lur'e Equations: Inner-Outer Factorization via Lur'e Equations
  Timo Reis, Matthias Voigt
  Pamm. https://doi.org/10.1002/pamm.201610403
• Reprint of “The Kalman–Yakubovich–Popov inequality for differential-algebraic systems: Existence of nonpositive solutions”
  Timo Reis, Matthias Voigt
  Systems & Control Letters. https://doi.org/10.1016/j.sysconle.2016.05.010

2015

• Distance Problems for Linear Dynamical Systems
  Daniel Kressner, Matthias Voigt
  Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory. https://doi.org/10.1007/978-3-319-15260-8_20
• Numerical Linear Algebra Methods for Linear Differential-Algebraic Equations
  Peter Benner, Philip Losse, Volker Mehrmann, Matthias Voigt
  Surveys in Differential-Algebraic Equations III. https://doi.org/10.1007/978-3-319-22428-2_3
• On linear-quadratic optimal control and robustness of differential-algebraic systems
• The Kalman-Yakubovich-Popov Inequality for Descriptor Systems: The Kalman-Yakubovich-Popov Inequality for Descriptor Systems
  Timo Reis, Matthias Voigt
  Pamm. https://doi.org/10.1002/pamm.201510312
• The Kalman–Yakubovich–Popov inequality for differential-algebraic systems
  Timo Reis, Olaf Rendel, Matthias Voigt
  Linear Algebra and its Applications. https://doi.org/10.1016/j.laa.2015.06.021
• The Kalman–Yakubovich–Popov inequality for differential-algebraic systems: Existence of nonpositive solutions
  Timo Reis, Matthias Voigt
  Systems & Control Letters. https://doi.org/10.1016/j.sysconle.2015.09.003

2014

• A structured pseudospectral method for ℋ∞-norm computation of large-scale descriptor systems
  Peter Benner, Matthias Voigt
  Mathematics of Control, Signals, and Systems. https://doi.org/10.1007/s00498-013-0121-7
• Computation of the ℋ∞-norm for large-scale systems
  Peter Benner, Ryan Lowe, Matthias Voigt
  Oberwolfach Reports. https://doi.org/10.4171/OWR/2013/56
• Solution of Descriptor Lur'e Equations via Even Matrix Pencils
  Timo Reis, Matthias Voigt
  Pamm. https://doi.org/10.1002/pamm.201410443
• The Dissipation Inequality for Differential-Algebraic Systems
  Timo Reis, Matthias Voigt
  Pamm. https://doi.org/10.1002/pamm.201410004

2013

• MB04BV – A FORTRAN 77 subroutine to compute the eigenvectors associated to the purely imaginary eigenvalues of skew-Hamiltonian/Hamiltonian matrix pencils
  Peihong Jiang, Matthias Voigt
  Niconet e. V.
• Spectral characterization and enforcement of negative imaginariness for descriptor systems
  Peter Benner, Matthias Voigt
  Linear Algebra and its Applications. https://doi.org/10.1016/j.laa.2012.12.044
• Spectral conditions for symmetric positive real and negative imaginary systems
  Naim Bajcinca, Matthias Voigt
  2013 European Control Conference (ECC). https://doi.org/10.23919/ecc.2013.6669824

2012

• Linear-quadratic infinite time horizon optimal control for differential- algebraic equations - a new algebraic criterion
  Timo Reis, Matthias Voigt
  20th International Symposium on Mathematical Theory of Networks and Systems (MTNS)
• Numerical computation of structured complex stability radii of large-scale matrices and pencils
  Peter Benner, Matthias Voigt
  2012 IEEE 51st IEEE Conference on Decision and Control (CDC). https://doi.org/10.1109/cdc.2012.6426906
• Robust and Efficient Algorithms for ℒ∞-Norm Computation for Descriptor Systems
  P. Benner, V. Sima, M. Voigt
  IFAC Proceedings Volumes. https://doi.org/10.3182/20120620-3-dk-2025.00114
• ℋ∞-Norm Computation for Large and Sparse Descriptor Systems
  Peter Benner, Matthias Voigt
  Pamm. https://doi.org/10.1002/pamm.201210383
• ℒ∞-Norm Computation for Continuous-Time Descriptor Systems Using Structured Matrix Pencils
  P. Benner, V. Sima, M. Voigt
  IEEE Transactions on Automatic Control. https://doi.org/10.1109/tac.2011.2161833

2011

• On the Computation of Particular Eigenvectors of Hamiltonian Matrix Pencils: On the Computation of Particular Eigenvectors of Hamiltonian Matrix Pencils
  Peter Benner, Matthias Voigt
  Pamm. https://doi.org/10.1002/pamm.201110366

2010

• ℒ∞-Norm Computation for Descriptor Systems
  Matthias Voigt