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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 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 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 work, we present a nonlinear model reduction approach for reducing two commonly used nonlinear dynamical models of power grids: the effective network (EN) model and the synchronous motor (SM) model. Such models are essential in…

Systems and Control · Electrical Eng. & Systems 2020-05-27 Tobias K. S. Ritschel , Frances Weiß , Manuel Baumann , Sara Grundel

We analyze a structure-preserving model order reduction technique for delay and stochastic delay equations based on the balanced truncation method and provide a system theoretic interpretation. Transferring error bounds based on Hankel…

Optimization and Control · Mathematics 2020-08-28 Simon Becker , Lorenz Richter

The Loewner framework for model reduction is extended to the class of linear switched systems. One advantage of this framework is that it introduces a trade-off between accuracy and complexity. Moreover, through this procedure, one can…

Numerical Analysis · Mathematics 2017-12-18 Ion Victor Gosea , Mihaly Petreczky , Athanasios C. Antoulas

In this paper, balancing based model order reduction (MOR) for large-scale linear discrete-time time-invariant systems in prescribed finite time intervals is studied. The first main topic is the development of error bounds regarding the…

Numerical Analysis · Mathematics 2019-02-06 Igor Pontes Duff , Patrick Kürschner

The interplay of positive and negative feedback loops on different time scales appears to be a fundamental mechanisms for robust and tunable oscillations in both biological systems and electro-mechanical systems. We develop a detailed…

Systems and Control · Electrical Eng. & Systems 2021-04-06 Weiming Che , Fulvio Forni

Model reduction is a central topic in systems biology and dynamical systems theory, for reducing the complexity of detailed models, finding important parameters, and developing multi-scale models for instance. While perturbation theory is a…

Molecular Networks · Quantitative Biology 2014-01-27 Sylvain Soliman , Francois Fages , Ovidiu Radulescu

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

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

Suppressing vibrations in mechanical systems, usually described by second-order dynamical models, is a challenging task in mechanical engineering in terms of computational resources even nowadays. One remedy is structure-preserving model…

Optimization and Control · Mathematics 2023-09-25 Rebekka S. Beddig , Peter Benner , Ines Dorschky , Timo Reis , Paul Schwerdtner , Matthias Voigt , Steffen W. R. Werner

In this article, we show that the projection-free, snapshot-based, balanced truncation method can be applied directly to unstable systems. We prove that even for unstable systems, the unmodified balanced proper orthogonal decomposition…

Fluid Dynamics · Physics 2015-08-27 Thibault L. B. Flinois , Aimee S. Morgans , Peter J. Schmid

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

Controllability and observability energy functions play a fundamental role in model order reduction and are inherently connected to optimal control problems. For linear dynamical systems the energy functions are known to be quadratic…

Dynamical Systems · Mathematics 2025-02-11 Linus Balicki , Serkan Gugercin

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

In this paper we consider different model reduction techniques for systems with moving loads. Due to the time-dependency of the input and output matrices, the application of time-varying projection matrices for the reduction offers new…

Dynamical Systems · Mathematics 2016-07-12 Maria Cruz Varona , Boris Lohmann

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

Model reduction plays a critical role in system control, with established methods such as balanced truncation widely used for linear systems. However, extending these methods to nonlinear settings, particularly polynomial dynamical systems…

Dynamical Systems · Mathematics 2025-06-25 Xin Mao , Can Chen

In real-world geophysical applications (such as predicting the climate change), the reduced models of real-world complex multiscale dynamics are used to predict the response of the actual multiscale climate to changes in various global…

Dynamical Systems · Mathematics 2013-07-30 Rafail V. Abramov , Marc P. Kjerland