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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

We introduce an algorithm based on a method of snapshots for computing approximate balanced truncations for discrete-time, stable, linear time-periodic systems. By construction, this algorithm is applicable to very high-dimensional systems,…

Optimization and Control · Mathematics 2007-08-06 Zhanhua Ma , Clarence W. Rowley , Gilead Tadmor

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

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

As a special type of bilinear systems, K-power bilinear systems possess a special coupled structure along with nice properties in practice. In this paper, we investigate the data-driven counterpart of balanced truncation for K-power…

Optimization and Control · Mathematics 2026-04-14 Xiaolong Wang , Biaolin Li , Xiaoli Wang

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 develop a pivot-shifted Carleman linearization framework for quantum algorithms solving quadratic nonlinear ordinary differential equations. By shifting the dynamics by a pivot state prior to Carleman lifting, and combining this with a…

Quantum Physics · Physics 2026-05-20 Ke Wang , Zikang Jia , Shravan Veerapaneni , Zhiyan Ding

We present a novel reformulation of balanced truncation, a classical model reduction method. The principal innovation that we introduce comes through the use of system response data that has been either measured or computed, without…

Numerical Analysis · Mathematics 2021-10-26 Ion Victor Gosea , Serkan Gugercin , Christopher Beattie

Balanced truncation (BT) is a model reduction method that utilizes a coordinate transformation to retain eigen-directions that are highly observable and reachable. To address realizability and scalability of BT applied to highly stiff and…

Systems and Control · Electrical Eng. & Systems 2022-07-13 Elnaz Rezaian , Cheng Huang , Karthik Duraisamy

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 show that two widely accepted model reduction techniques, Balanced Truncation and Balanced Singular Perturbation Approximation, can be derived as limiting approximations of a carefully constructed parameterization of Linear Time…

Optimization and Control · Mathematics 2019-01-10 Philip E. Paré , David Grimsman , Alma T. Wilson , Mark K. Transtrum , Sean Warnick

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 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

In recent years, quaternion matrix completion (QMC) based on low-rank regularization has been gradually used in image de-noising and de-blurring.Unlike low-rank matrix completion (LRMC) which handles RGB images by recovering each color…

Image and Video Processing · Electrical Eng. & Systems 2021-01-08 Liqiao Yang , Kit Ian Kou , Jifei Miao

We develop a structure-preserving system-theoretic model reduction framework for nonlinear power grid networks. First, via a lifting transformation, we convert the original nonlinear system with trigonometric nonlinearities to an equivalent…

Systems and Control · Electrical Eng. & Systems 2022-03-18 Bita Safaee , Serkan Gugercin

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

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

We provide an analytical framework for balanced realization model order reduction of linear control systems which depend on an unknown parameter. Besides recovering known results for the first order corrections, we obtain explicit novel…

Systems and Control · Computer Science 2016-06-24 Carles Batlle , Nestor Roqueiro

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

We present a new balancing-based structure-preserving model reduction technique for linear port-Hamiltonian descriptor systems. The proposed method relies on a modification of a set of two dual generalized algebraic Riccati equations that…

Optimization and Control · Mathematics 2024-09-18 Tobias Breiten , Philipp Schulze