Control theory is one of the most rapidly developing disciplines of mathematics and
engineering in the second half of the 20th century. In the past decade, implementations of …

We study large‐scale, continuous‐time linear time‐invariant control systems with a sparse or
structured state matrix and a relatively small number of inputs and outputs. The main …

Abstract Model order reduction of large–scale linear time–invariant systems is an
omnipresent task in control and simulation of complex dynamical processes. The solution of …

To implement the balancing based model reduction of large-scale dynamical systems we
need to compute the low-rank (controllability and observability) Gramian factors by solving …

Die Lösung von Matrixgleichungen wie Riccati-Gleichungen, Lyapunov-Gleichungen und
Sylvester-Gleichungen wird in vielen Gebieten der angewandten Mathematik benötigt: Für …

In this thesis, we investigate the numerical solution of large-scale, algebraic matrix
equations. The focus lies on numerical methods based on the alternating directions implicit …

We present a new method for the computation of low rank approximations to the solution of
large, sparse, stable Lyapunov equations. It is based on a generalization of the classical …

State-of-the-art, uni-processor algebraic Riccati equation solvers for automatic control
computations are investigated and compared for various problem sizes. General-purpose …

The authors present several algorithms that compute approximate solutions to the Lyapunov
equation AX+ XA/sup T/+ BB/sup T/= 0 and the algebraic Riccati equation A/sup T/X+ XA …

A few methods are proposed for solving large Lyapunov equations that arise in control
problems. The common case where the right hand side is a small rank matrix is considered …