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Balanced truncation is a well-established model order reduction method which has been applied to a variety of problems. Recently, a connection between linear Gaussian Bayesian inference problems and the system-theoretic concept of balanced…

Numerical Analysis · Mathematics 2024-01-04 Josie König , Melina A. Freitag

We consider model order reduction of a nonlinear cable-mass system modeled by a 1D wave equation with interior damping and dynamic boundary conditions. The system is driven by a time dependent forcing input to a linear mass-spring system at…

Optimization and Control · Mathematics 2018-11-27 Belinda A. Batten , Hesam Shoori , John R. Singler , Madhuka H. Weerasinghe

A standard approach for model reduction of linear input-output systems is balanced truncation, which is based on the controllability and observability properties of the underlying system. The related dominant subspace projection model…

Optimization and Control · Mathematics 2019-08-23 Peter Benner , Christian Himpe

Novel constructions of empirical controllability and observability gramians for nonlinear systems for subsequent use in a balanced truncation style of model reduction are proposed. The new gramians are based on a generalisation of the…

Optimization and Control · Mathematics 2007-05-23 Marissa Condon , Rossen I. Ivanov

Structured reduced-order modeling is a central component in the computer-aided design of control systems in which cheap-to-evaluate low-dimensional models with physically meaningful internal structures are computed. In this work, we develop…

Numerical Analysis · Mathematics 2026-05-25 Sean Reiter , Steffen W. R. Werner

This paper discusses model order reduction of LTI systems over limited frequency intervals within the framework of balanced truncation. Two new \emph{frequency-dependent balanced truncation} methods were developed, one is \emph{SF-type…

Systems and Control · Computer Science 2016-02-16 Xin Du , Peter Benner

The paper presents a model reduction framework geared towards the analysis and design of systems that switch and oscillate. While such phenomena are ubiquitous in nature and engineering, model reduction methods are not well developed for…

Systems and Control · Electrical Eng. & Systems 2020-05-19 Alberto Padoan , Fulvio Forni , Rodolphe Sepulchre

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 and the Volterra series formulation for QB systems. We…

Numerical Analysis · Mathematics 2017-05-17 Peter Benner , Pawan Goyal , Serkan Gugercin

A nonintrusive model order reduction method for bilinear stochastic differential equations with additive noise is proposed. A reduced order model (ROM) is designed in order to approximate the statistical properties of high-dimensional…

Numerical Analysis · Mathematics 2025-06-11 M. A. Freitag , J. M. Nicolaus , M. Redmann

We consider a second-order linear system of ordinary differential equations (ODEs) including random variables. A stochastic Galerkin method yields a larger deterministic linear system of ODEs. We apply a model order reduction (MOR) of this…

Numerical Analysis · Mathematics 2023-07-11 Roland Pulch

We develop the framework for a non-intrusive, quadrature-based method for approximate balanced truncation (QuadBT) of linear systems with quadratic outputs, thus extending the applicability of QuadBT, which was originally designed for…

Numerical Analysis · Mathematics 2025-09-17 Reetish Padhi , Ion Victor Gosea , Igor Pontes Duff , Serkan Gugercin

This paper deals with non-Lipschitz nonlinear systems. Such systems can be approximated by a linear map of so-called signatures, which play a crucial role in the theory of rough paths and can be interpreted as collections of iterated…

Optimization and Control · Mathematics 2025-11-07 Martin Redmann , Justus Werner

Model order reduction algorithms for large-scale descriptor systems are proposed using balanced truncation, in which symmetry or block skew symmetry (reciprocity) and the positive realness of the original transfer matrix are preserved. Two…

Numerical Analysis · Computer Science 2018-11-13 Yuichi Tanji

We consider the problem of constructing reduced models for large scale systems with poles in general domains in the complex plane (as opposed to, e.g., the open left-half plane or the open unit disk). Our goal is to design a model reduction…

Numerical Analysis · Mathematics 2025-02-10 Alessandro Borghi , Tobias Breiten , Serkan Gugercin

This paper proposes a data-driven model reduction approach on the basis of noisy data. Firstly, the concept of data reduction is introduced. In particular, we show that the set of reduced-order models obtained by applying a Petrov-Galerkin…

Optimization and Control · Mathematics 2022-02-01 Azka Muji Burohman , Bart Besselink , Jacquelien M. A. Scherpen , M. Kanat Camlibel

We deduce a procedure to apply balanced truncation to parameter-dependent differential-algebraic systems. For that we solve multiple projected Lyapunov equations for different parameter values to compute the Gramians that are required for…

Dynamical Systems · Mathematics 2024-01-08 Jennifer Przybilla , Matthias Voigt

In this article, we propose a novel discretization method based on numerical integration for discretizing continuous systems, termed the $\alpha\beta$-approximation or Scalable Bilinear Transformation (SBT). In contrast to existing methods,…

Systems and Control · Electrical Eng. & Systems 2026-01-15 Shen Chen , Chaohou Liu , Wei Yao , Jisong Wang , Shuaipo Guo , Zeng Liu , Jinjun Liu

In this work, we study projection-based model order reduction (MOR) for switched linear systems (SLS) in control form, where the projection matrices are obtained from the solutions of generalized Lyapunov equations (GLEs). We investigate…

Numerical Analysis · Mathematics 2026-05-18 Mattia Manucci , Benjamin Unger

In this paper, we prove several new results that give new insights into bilinear systems. We discuss conditions for asymptotic stability using probabilistic arguments. Moreover, we provide a global characterization of reachability in…

Numerical Analysis · Mathematics 2021-04-02 Martin Redmann

Linear time-invariant quadratic output (LTIQO) systems generalize linear time-invariant systems to nonlinear regimes. Problems of this class occur in multiple applications naturally, such as port-Hamiltonian systems, optimal control, and…

Optimization and Control · Mathematics 2025-05-20 Birgit Hillebrecht , Benjamin Unger