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We propose a model order reduction approach for balanced truncation of linear switched systems. Such systems switch among a finite number of linear subsystems or modes. We compute pairs of controllability and observability Gramians…

Numerical Analysis · Mathematics 2017-12-07 Ion Victor Gosea , Mihaly Petreczky , Athanasios C. Antoulas , Christophe Fiter

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

Model order reduction involves constructing a reduced-order approximation of a high-order model while retaining its essential characteristics. This reduced-order model serves as a substitute for the original one in various applications such…

Systems and Control · Electrical Eng. & Systems 2024-03-06 Qiu-Yan Song , Umair Zulfiqar , Zhi-Hua Xiao , Mohammad Monir Uddin , Victor Sreeram

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

In this paper, we propose new algebraic Gramians for continuous-time linear switched systems, which satisfy generalized Lyapunov equations. The main contribution of this work is twofold. First, we show that the ranges of those Gramians…

Optimization and Control · Mathematics 2018-06-04 Igor Pontes Duff , Sara Grundel , Peter Benner

This paper presents a novel model order reduction framework tailored for fully nonlinear stochastic dynamics without lifting them to quadratic systems and without using linearization techniques. By directly leveraging structural properties…

Probability · Mathematics 2025-08-05 Martin Redmann

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

We present a balanced truncation model reduction approach for a class of nonlinear systems with time-varying and uncertain inputs. First, our approach brings the nonlinear system into quadratic-bilinear~(QB) form via a process called…

Numerical Analysis · Mathematics 2020-10-29 Boris Kramer , Karen E. Willcox

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

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

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 paper, we present an empirical balanced truncation method for nonlinear systems with linear time-invariant input vector field components. First, we define differential reachability and observability Gramians. They are matrix valued…

Systems and Control · Computer Science 2019-10-30 Yu Kawano , Jacquelien M. A. Scherpen

We consider the Bayesian approach to the linear Gaussian inference problem of inferring the initial condition of a linear dynamical system from noisy output measurements taken after the initial time. In practical applications, the large…

Systems and Control · Electrical Eng. & Systems 2021-11-29 Elizabeth Qian , Jemima M. Tabeart , Christopher Beattie , Serkan Gugercin , Jiahua Jiang , Peter R. Kramer , Akil Narayan

Model reduction is a powerful tool in dealing with numerical simulation of large scale dynamic systems for studying complex physical systems. Two major types of model reduction methods for linear time-invariant dynamic systems are Krylov…

Numerical Analysis · Mathematics 2024-06-11 Lei-Hong Zhang , Ren-Cang Li

In this paper, we consider the problem of quantifying controllability and observability of a nonlinear discrete time dynamical system. We introduce the Koopman operator as a canonical representation of the system and apply a lifting…

Systems and Control · Computer Science 2017-09-27 Enoch Yeung , Zhiyuan Liu , Nathan O. Hodas

This paper studies model order reduction of multi-agent systems consisting of identical linear passive subsystems, where the interconnection topology is characterized by an undirected weighted graph. Balanced truncation based on a pair of…

Optimization and Control · Mathematics 2019-01-29 Xiaodong Cheng , Jacquelien M. A. Scherpen , Bart Besselink

In this paper, we present a theoretical analysis of the model reduction algorithm for linear switched systems. This algorithm is a reminiscence of the balanced truncation method for linear parameter varying systems. Specifically in this…

Optimization and Control · Mathematics 2013-03-19 Mihaly Petreczky , Rafael Wisniewski , John Leth

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 concerns the recently proposed quasi-balanced truncation model reduction method for linear quantum stochastic systems. It has previously been shown that the quasi-balanceable class of systems (i.e. systems that can be truncated…

Quantum Physics · Physics 2014-08-11 Onvaree Techakesari , Hendra I. Nurdin

This paper studies the data-driven balanced truncation (BT) method for second-order systems based on the measurements in the frequency domain. The basic idea is to approximate Gramians used the numerical quadrature rules, and establish the…

Numerical Analysis · Mathematics 2025-06-05 Xiaolong Wang , Xuerong Yang , Xiaoli Wang , Bo Song
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