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The paper proposes a model reduction algorithm for linear hybrid systems, i.e., hybrid systems with externally induced discrete events, with linear continuous subsystems, and linear reset maps. The model reduction algorithm is based on…

Dynamical Systems · Mathematics 2020-03-19 Ion Victor Gosea , Mihaly Petreczky , John Leth , Rafael Wisniewski , Athanasios C. Antoulas

Model order reduction is a technique that is used to construct low-order approximations of large-scale dynamical systems. In this paper, we investigate a balancing based model order reduction method for dynamical systems with a linear…

Optimization and Control · Mathematics 2019-09-11 Peter Benner , Pawan Goyal , Igor Pontes Duff

This paper proposes a balancing-based model reduction approach for an interconnection of passive dynamic subsystems. This approach preserves the passivity and stability of both the subsystems and the interconnected system. Hereto, one…

Systems and Control · Electrical Eng. & Systems 2023-11-23 Luuk Poort , Bart Besselink , Rob H. B. Fey , Nathan van de Wouw

Dynamical systems with quadratic outputs have recently attracted significant attention. In this paper, we consider bilinear dynamical systems, a special class of weakly nonlinear systems, with a quadratic output. We develop various…

Numerical Analysis · Mathematics 2025-07-08 Heike Faßbender , Serkan Gugercin , Till Peters

We derive a mixed-dimensional 3D-1D formulation of the electrostatic equation in two domains with different dielectric constants to compute, with an affordable computational cost, the electric field and potential in the relevant case of…

Numerical Analysis · Mathematics 2024-10-07 Beatrice Crippa , Anna Scotti , Andrea Villa

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

We consider systems of nonlinear magnetostatics and quasistatics that typically arise in the modeling and simulation of electric machines. The nonlinear problems, eventually obtained after time discretization, are usually solved by…

Numerical Analysis · Mathematics 2023-11-27 Herbert Egger , Felix Engertsberger , Bogdan Radu

When balanced truncation is used for model order reduction, one has to solve a pair of Lyapunov equations for two Gramians and uses them to construct a reduced-order model. Although advances in solving such equations have been made, it is…

Numerical Analysis · Mathematics 2020-03-11 Nguyen Thanh Son , Pierre-Yves Gousenbourger , Estelle Massart , Tatjana Stykel

The increasing integration of power electronic devices is driving the development of more advanced tools and methods for the modeling, analysis, and control of modern power systems to cope with the different time-scale oscillations. In this…

Systems and Control · Electrical Eng. & Systems 2019-10-22 Umberto Biccari , Noboru Sakamoto , Eneko Unamuno , Danel Madariaga , Enrique Zuazua , Jon Andoni Barrena

This work discusses model reduction for differential-algebraic systems with quadratic output equations. Under mild conditions, these systems can be transformed into a Weierstra{\ss} canonical form and, thus, be decoupled into differential…

Dynamical Systems · Mathematics 2024-02-23 Jennifer Przybilla , Igor Pontes Duff , Pawan Goyal , Peter Benner

Magnetizable piezoelectric beams exhibit strong couplings between mechanical, electric, and magnetic fields, significantly affecting their high-frequency vibrational behavior. Ensuring exponential stability under boundary feedback…

Numerical Analysis · Mathematics 2026-04-07 Ahmet Kaan Aydin , Ahmet Ozkan Ozer , Jacob Walterman

This paper addresses the problem of frequency-weighted extended balanced truncation for discrete and continuous-time linear time-invariant plants. We show that the frequency-weighted discrete-time plant admits block-diagonal solutions to…

Systems and Control · Electrical Eng. & Systems 2025-12-03 Sribalaji C. Anand , Henrik Sandberg

Balanced truncation is one of the most common model order reduction schemes. In this paper, we study finite-frequency model order reduction (FF-MOR) problems of linear continuous-time systems within the framework of balanced truncation…

Systems and Control · Computer Science 2017-03-21 Xin Du , Peter Benner

In this paper, we explore the role of tensor algebra in balanced truncation (BT) based model reduction/identification for high-dimensional multilinear/linear time invariant systems. In particular, we employ tensor train decomposition (TTD),…

Systems and Control · Electrical Eng. & Systems 2020-01-28 Can Chen , Amit Surana , Anthony Bloch , Indika Rajapakse

In this paper, we investigate a large-scale stochastic system with bilinear drift and linear diffusion term. Such high dimensional systems appear for example when discretizing a stochastic partial differential equations in space. We study a…

Optimization and Control · Mathematics 2018-04-06 Martin Redmann

In this paper, we rigorously investigate the truncation method for the Cauchy problem of Helmholtz equations which is widely used to model propagation phenomena in physical applications. The method is a well-known approach to the…

Analysis of PDEs · Mathematics 2016-03-15 Huy Tuan Nguyen , Vo Anh Khoa , Mach Nguyet Minh , Thanh Tran

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

Optimization and Control · Mathematics 2021-05-17 Peter Benner , Steffen W. R. Werner

We construct a cut finite element method for the membrane elasticity problem on an embedded mesh using tangential differential calculus. Both free membranes and membranes coupled to 3D elasticity are considered. The discretization comes…

Numerical Analysis · Mathematics 2016-08-24 Mirza Cenanovic , Peter Hansbo , Mats G. Larson

We consider a~quasilinear model arising from dynamical magnetization. This model is described by a~magneto-quasistatic (MQS) approximation of Maxwell's equations. Assuming that the medium consists of a~conducting and a~non-conducting part,…

Analysis of PDEs · Mathematics 2022-06-01 Ralph Chill , Timo Reis , Tatjana Stykel

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