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The quadrature-based balanced truncation (QuadBT) framework of arXiv:2104.01006 is a non-intrusive reformulation of balanced truncation (BT), a classical projection-based model-order reduction technique for linear systems. QuadBT is…

Numerical Analysis · Mathematics 2025-08-26 Sean Reiter , Ion Victor Gosea , Serkan Gugercin

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 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

Quadrature-based approximation of Gramians in standard balanced truncation yields a non-intrusive, data-driven implementation that requires only transfer function samples on the imaginary axis, which can be measured experimentally. This…

Systems and Control · Electrical Eng. & Systems 2026-03-24 Umair Zulfiqar , Qiu-Yan Song , Zhi-Hua Xiao , Victor Sreeram

When solving partial differential equations numerically, usually a high order spatial discretisation is needed. Model order reduction (MOR) techniques are often used to reduce the order of spatially-discretised systems and hence reduce…

Optimization and Control · Mathematics 2017-09-19 Martin Redmann

The theory of nonlinear balanced truncation provides a system-theoretic framework for model reduction that preserves important properties such as stability, controllability, and observability. We present a scalable algorithm for computing…

Optimization and Control · Mathematics 2026-04-28 Nicholas A. Corbin , Boris Kramer

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

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

As an alternative to the popular balanced truncation method, the cross Gramian matrix induces a class of balancing model reduction techniques. Besides the classical computation of the cross Gramian by a Sylvester matrix equation, an…

Optimization and Control · Mathematics 2016-06-14 Christian Himpe , Mario Ohlberger

We introduce a data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves…

Optimization and Control · Mathematics 2016-04-04 Jake Bouvrie , Boumediene Hamzi

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

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

In this paper, nonlinear model reduction for power systems is performed by the balancing of empirical controllability and observability covariances that are calculated around the operating region. Unlike existing model reduction methods,…

Systems and Control · Computer Science 2016-08-30 Junjian Qi , Jianhui Wang , Hui Liu , Aleksandar D. Dimitrovski

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 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

Nonlinear balanced truncation is a model order reduction technique that reduces the dimension of nonlinear systems in a manner that accounts for either open- or closed-loop observability and controllability aspects of the system. Two…

Optimization and Control · Mathematics 2023-02-07 Boris Kramer , Serkan Gugercin , Jeff Borggaard

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

This paper introduces a quadrature-free, non-intrusive approach to balanced truncation for both continuous-time and discrete-time systems. The method non-intrusively constructs reduced-order models using available transfer function samples…

Systems and Control · Electrical Eng. & Systems 2026-02-20 Umair Zulfiqar

This paper deals with the balanced truncation model reduction of discrete-time, linear time-varying, heterogeneous subsystems interconnected over finite arbitrary directed graphs. The information transfer between the subsystems is subject…

Optimization and Control · Mathematics 2017-08-15 Dany Abou Jaoude , Mazen Farhood

Model order reduction plays a crucial role in simplifying complex systems while preserving their essential dynamic characteristics, making it an invaluable tool in a wide range of applications, including robotic systems, signal processing,…

Systems and Control · Electrical Eng. & Systems 2025-04-22 Shenghan Mei , Ziqin He , Yidan Mei , Xin Mao , Anqi Dong , Ren Wang , Can Chen