Extended balancing of continuous LTI systems

a structure-preserving approach

Journal article (2023)

Authors

L.P. Borja Rosales Learning & Autonomous Control - Mechanical, Maritime and Materials Engineering
Jacquelien M.A. Scherpen Rijksuniversiteit Groningen
Kenji Fujimoto Kyoto University
Research Group
Learning & Autonomous Control (Mechanical, Maritime and Materials Engineering) (TU Delft)
Copyright: © 2023 L.P. Borja Rosales, Jacquelien M.A. Scherpen, Kenji Fujimoto
DOI
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https://doi.org/10.1109/TAC.2021.3138645
Model reduction Port-Hamiltonian systems Controllability Linear systems Observability Standards Symmetric matrices Error bound Extended Gramians Linear matrix inequalities Reduced order systems
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Published Date

2023

Language

English

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Faculty

Mechanical, Maritime and Materials Engineering

Department

Cognitive Robotics

Research Group

Learning & Autonomous Control

Abstract

In this article, we treat extended balancing for continuous-time linear time-invariant systems. We take a dissipativity perspective, thus, resulting in a characterization in terms of linear matrix inequalities. This perspective is useful for determining a priori error bounds. In addition, we address the problem of structure-preserving model reduction of the subclass of port-Hamiltonian systems. We establish sufficient conditions to ensure that the reduced-order model preserves a port-Hamiltonian structure. Moreover, we show that the use of extended Gramians can be exploited to get a small error bound and, possibly, to preserve a physical interpretation for the reduced-order model. We illustrate the results with a large-scale mechanical system example. Furthermore, we show how to interpret a reduced-order model of an electrical circuit again as a lower dimensional electrical circuit.