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 …

Matrix equations are omnipresent in (numerical) linear algebra and systems theory.
Especially in model order reduction (MOR), they play a key role in many balancing-based …

The rational Krylov subspace method (RKSM) and the low-rank alternating directions implicit
(LR-ADI) iteration are established numerical tools for computing low-rank solution factors of …

This chapter provides an introduction to the concept of system balancing. An overview of the
historical development is given, and application areas for balancing-based model reduction …

Solving large-scale continuous-time algebraic Riccati equations is a significant challenge in
various control theory applications. This work demonstrates that when the matrix coefficients …

Output-based controllers are known to be fragile with respect to model uncertainties. The
standard H∞-control theory provides a general approach to robust controller design based …

One of the most computationally expensive steps of the low-rank ADI method for large-scale
Lyapunov equations is the solution of a shifted linear system at each iteration. We propose …

Many of the commonly used methods in model‐order reduction do not guarantee stability of
the reduced‐order model. This article extends the eigenvalue reassignment method of …

The nonsymmetric T-Riccati equation is a quadratic matrix equation where the linear part
corresponds to the so-called T-Sylvester or T-Lyapunov operator that has previously been …

We introduce a model reduction approach for linear time-invariant second order systems
based on positive real balanced truncation. Our method guarantees to preserve asymptotic …