Computational methods for linear matrix equations

V Simoncini - siam REVIEW, 2016 - SIAM
Given the square matrices A,B,D,E and the matrix C of conforming dimensions, we consider
the linear matrix equation A\mathbfXE+D\mathbfXB=C in the unknown matrix \mathbfX. Our …

Lyapunov equations, energy functionals, and model order reduction of bilinear and stochastic systems

P Benner, T Damm - SIAM journal on control and optimization, 2011 - SIAM
We discuss the relation of a certain type of generalized Lyapunov equations to Gramians of
stochastic and bilinear systems together with the corresponding energy functionals. While …

-Quasi-Optimal Model Order Reduction for Quadratic-Bilinear Control Systems

P Benner, P Goyal, S Gugercin - SIAM Journal on Matrix Analysis and …, 2018 - SIAM
We investigate the optimal model reduction problem for large-scale quadratic-bilinear (QB)
control systems. Our contributions are threefold. First, we discuss the variational analysis …

Balanced truncation model order reduction for quadratic-bilinear control systems

P Benner, P Goyal - arXiv preprint arXiv:1705.00160, 2017 - arxiv.org
We discuss balanced truncation model order reduction for large-scale quadratic-bilinear
(QB) systems. Balanced truncation for linear systems mainly involves the computation of the …

Balanced truncation for quadratic-bilinear control systems

P Benner, P Goyal - Advances in Computational Mathematics, 2024 - Springer
We discuss model order reduction (MOR) for large-scale quadratic-bilinear (QB) systems
based on balanced truncation. The method for linear systems mainly involves the …

Balanced averaging of bilinear systems with applications to stochastic control

C Hartmann, B Schafer-Bung, A Thons-Zueva - SIAM Journal on Control and …, 2013 - SIAM
We study balanced model reduction for stable bilinear systems in the limit of partly vanishing
Hankel singular values. We show that the dynamics can be split into a fast and a slow …

Nonlinear Balanced Truncation: Part 2--Model Reduction on Manifolds

B Kramer, S Gugercin, J Borggaard - arXiv preprint arXiv:2302.02036, 2023 - arxiv.org
Nonlinear balanced truncation is a model order reduction technique that reduces the
dimension of nonlinear systems in a manner that accounts for either open-or closed-loop …

Model order reduction based on system balancing

P Benner, T Breiten - Model Reduction and Approximation, 2017 - books.google.com
Weintroduce balancing-based model order reduction (MOR) techniques for large-scale
dynamical systems. We emphasize the efficient implementation of state-of-the-art techniques …

[HTML][HTML] Scalable computation of energy functions for nonlinear balanced truncation

B Kramer, S Gugercin, J Borggaard, L Balicki - Computer Methods in …, 2024 - Elsevier
Nonlinear balanced truncation is a model order reduction technique that reduces the
dimension of nonlinear systems in a manner that accounts for either open-or closed-loop …

Nonlinear balanced truncation: Part 1-Computing energy functions

B Kramer, S Gugercin, J Borggaard… - arXiv preprint arXiv …, 2022 - arxiv.org
Nonlinear balanced truncation is a model order reduction technique that reduces the
dimension of nonlinear systems in a manner that accounts for either open-or closed-loop …