The differential Sylvester equation and its symmetric version, the differential Lyapunov
equation, appear in different fields of applied mathematics like control theory, system theory …

In this article we investigate model order reduction of large-scale systems using frequency-
limited balanced truncation, which restricts the well known balanced truncation framework to …

In this paper, we discuss numerical methods for solving large-scale continuous-time
algebraic Riccati equations. These methods have been the focus of intensive research in …

The efficient numerical integration of large-scale matrix differential equations is a topical
problem in numerical analysis and of great importance in many applications. Standard …

We consider high-order splitting schemes for large-scale differential Riccati equations. Such
equations arise in many different areas and are especially important within the field of …

In this thesis, structure-preserving model order reduction for dynamical systems is studied.
The particular focus lies on mechanical systems described by differential equations with …

Considering the use of dynamical systems in practical applications, often only limited
regions in the time or frequency domain are of interest. Therefore, it usually pays off to …

The numerical analysis of linear quadratic regulator design problems for parabolic partial
differential equations requires solving Riccati equations. In the finite time horizon case, the …

In this paper, we first investigate the finite-frequency model order reduction for linear
systems based on low-rank Gramian approximations. An efficient algorithm for computing …

ABSTRACT A practical procedure based on implicit time integration methods applied to the
differential Lyapunov equations arising in the square root balanced truncation method is …