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Related papers: Balanced truncation for linear switched systems

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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

This work introduces the empirical cross gramian for multiple-input-multiple-output systems. The cross gramian is a tool for reducing the state space of control systems, which conjoins controllability and observability information into a…

Optimization and Control · Mathematics 2016-08-22 Christian Himpe , Mario Ohlberger

We consider linear dynamical systems consisting of ordinary differential equations with high dimensionality. The aim of model order reduction is to construct an approximating system of a much lower dimension. Therein, the reduced system may…

Numerical Analysis · Mathematics 2017-11-09 Roland Pulch

In this paper, the problem of full state approximation by model reduction is studied for stochastic and bilinear systems. Our proposed approach relies on identifying the dominant subspaces based on the reachability Gramian of a system. Once…

Numerical Analysis · Mathematics 2021-02-16 Martin Redmann , Igor Pontes Duff

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

In this paper, we treat extended balancing for continuous-time linear time-invariant systems, and we address the problem of structure-preserving model reduction of the subclass of port-Hamiltonian systems. We establish sufficient conditions…

Systems and Control · Electrical Eng. & Systems 2020-01-06 Pablo Borja , Jacquelien M. A. Scherpen , Kenji Fujimoto

Small signal analysis is a special case of analytical approaches using Taylor expansions of power system differential equations with the truncation performed at order one. The truncated Taylor expansions (TTEs) at higher orders can lead to…

Systems and Control · Computer Science 2018-11-05 Bin Wang , Xin Xu , Kai Sun

We consider model order reduction of a nonlinear cable-mass system modeled by a 1D wave equation with interior damping and dynamic boundary conditions. The system is driven by a time dependent forcing input to a linear mass-spring system at…

Optimization and Control · Mathematics 2018-11-27 Belinda A. Batten , Hesam Shoori , John R. Singler , Madhuka H. Weerasinghe

Data-driven reduced-order models often fail to make accurate forecasts of high-dimensional nonlinear dynamical systems that are sensitive along coordinates with low-variance because such coordinates are often truncated, e.g., by proper…

Systems and Control · Electrical Eng. & Systems 2023-04-14 Samuel E. Otto , Alberto Padovan , Clarence W. Rowley

We develop a linear systems theory that coincides with the existing theories for continuous and discrete dynamical systems, but that also extends to linear systems defined on nonuniform time domains. The approach here is based on…

Optimization and Control · Mathematics 2009-03-03 John M. Davis , Ian A. Gravagne , Billy J. Jackson , Robert J. Marks

In this paper, we consider model order reduction for bilinear systems with non-zero initial conditions. We discuss choices of Gramians for both the homogeneous and the inhomogeneous parts of the system individually and prove how these…

Numerical Analysis · Mathematics 2022-05-19 Martin Redmann , Igor Pontes Duff

Structured reduced-order modeling is a central component in the computer-aided design of control systems in which cheap-to-evaluate low-dimensional models with physically meaningful internal structures are computed. In this work, we develop…

Numerical Analysis · Mathematics 2026-05-25 Sean Reiter , Steffen W. R. Werner

Given a family of systems, identifying stabilizing switching signals in terms of infinite walks constructed by concatenating cycles on the underlying directed graph of a switched system that satisfy certain conditions, is a well-known…

Systems and Control · Computer Science 2020-05-18 Atreyee Kundu

This paper considers large-scale linear stochastic systems representing, e.g., spatially discretized stochastic partial differential equations. Since asymptotic stability can often not be ensured in such a stochastic setting (e.g. due to…

Numerical Analysis · Mathematics 2022-05-19 Martin Redmann , Nahid Jamshidi

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

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

The cross gramian matrix is a tool for model reduction and system identification, but it is only computable for square control systems. For symmetric systems the cross gramian possesses a useful relation to the system's associated Hankel…

Optimization and Control · Mathematics 2016-08-22 Christian Himpe , Mario Ohlberger

In this paper, we consider the problem of finding surrogate models for large-scale second-order linear time-invariant systems with inhomogeneous initial conditions. For this class of systems, the superposition principle allows us to…

Dynamical Systems · Mathematics 2022-06-24 Jennifer Przybilla , Igor Pontes Duff , Peter Benner

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 develop and analyze an integral fixed-time sliding mode control method for a scenario in which the system model is only partially known, utilizing Gaussian processes. We present two theorems on fixed-time convergence. The…

Systems and Control · Electrical Eng. & Systems 2025-05-30 Chaimae El Mortajinea , Moussa Labbadib , Adnane Saoudc , Mostafa Bouzia