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A bilinear \(\mathcal {H}_{2}\) model order reduction approach to linear parameter-varying systems

  • Peter Benner
  • Xingang CaoEmail author
  • Wil Schilders
Open Access
Article
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Part of the following topical collections:
  1. Model reduction of parametrized Systems

Abstract

This paper focuses on the model reduction problem for a special class of linear parameter-varying systems. This kind of systems can be reformulated as bilinear dynamical systems. Based on the bilinear system theory, we give a definition of the \(\mathcal {H}_{2}\) norm in the generalized frequency domain. Then, a model reduction method is proposed based on the gradient descent on the Grassmann manifold. The merit of the method is that by utilizing the gradient flow analysis, the algorithm is guaranteed to converge, and further speedup of the convergence rate can be achieved as well. Two numerical examples are tested to demonstrate the proposed method.

Keywords

Model order reduction Linear parameter-varying systems Bilinear dynamical systems Gradient descent Grassmann manifold 

Mathematics Subject Classification (2010)

14M15 34C20 65K10 93C10 

Notes

Acknowledgments

The authors would like to thank the European Cost Action: TD1307-European Model Reduction Network (EU-MORNET) for the funding of a short-term scientific mission, which leads to this work.

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Copyright information

© The Author(s) 2019

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Computational Methods in Systems and Control TheoryMax Planck Institute for Dynamics of Complex Technical SystemsMagdeburgGermany
  2. 2.Centre for Analysis, Scientific Computing and ApplicationsEindhoven University of TechnologyEindhovenThe Netherlands

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