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 …
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
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 …
stochastic and bilinear systems together with the corresponding energy functionals. While …
-Quasi-Optimal Model Order Reduction for Quadratic-Bilinear Control Systems
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 …
control systems. Our contributions are threefold. First, we discuss the variational analysis …
Balanced truncation model order reduction for quadratic-bilinear control systems
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 …
(QB) systems. Balanced truncation for linear systems mainly involves the computation of the …
Balanced truncation for quadratic-bilinear control systems
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 …
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 …
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
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 …
dimension of nonlinear systems in a manner that accounts for either open-or closed-loop …
Model order reduction based on system balancing
Weintroduce balancing-based model order reduction (MOR) techniques for large-scale
dynamical systems. We emphasize the efficient implementation of state-of-the-art techniques …
dynamical systems. We emphasize the efficient implementation of state-of-the-art techniques …
[HTML][HTML] Scalable computation of energy functions for nonlinear balanced truncation
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 …
dimension of nonlinear systems in a manner that accounts for either open-or closed-loop …
Nonlinear balanced truncation: Part 1-Computing energy functions
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 …
dimension of nonlinear systems in a manner that accounts for either open-or closed-loop …