A novel Krylov method for model order reduction of quadratic bilinear systems

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Abstract

A novel Krylov subspace method is proposed to substantially reduce the computational complexity of the special class of quadratic bilinear dynamical systems. Based on the first two generalized transfer functions of the system, a Petrov-Galerkin projection scheme is applied. It is shown that such a projection amounts to interpolating the transfer functions at specific points which, in fact, is equivalent to constructing the corresponding Krylov subspace. For single-input single-output systems, the relevant Krylov subspace can be readily constructed for the interpolation points. For multi-input multi-output systems, also user-specified directional information is required so that a tangential interpolation can be determined. The method is demonstrated by numerical examples.

Original languageEnglish
Title of host publication2018 IEEE Conference on Decision and Control, CDC 2018
PublisherInstitute of Electrical and Electronics Engineers
Pages3217-3222
Number of pages6
ISBN (Electronic)9781538613955
DOIs
Publication statusPublished - 18 Jan 2019
Event57th IEEE Conference on Decision and Control, (CDC2018) - Miami, United States
Duration: 17 Dec 201819 Dec 2018
Conference number: 57

Conference

Conference57th IEEE Conference on Decision and Control, (CDC2018)
Abbreviated titleCDC 2018
CountryUnited States
CityMiami
Period17/12/1819/12/18

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Keywords

  • Model order reduction
  • Krylov methods
  • Quadratic-bilinear systems

Cite this

Cao, X., Maubach, J. M. L., Weiland, S., & Schilders, W. H. A. (2019). A novel Krylov method for model order reduction of quadratic bilinear systems. In 2018 IEEE Conference on Decision and Control, CDC 2018 (pp. 3217-3222). [8619575] Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/CDC.2018.8619575