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An Extension to Balanced Truncation With Application to Structured Model Reduction
KTH, School of Electrical Engineering (EES), Automatic Control.ORCID iD: 0000-0003-1835-2963
2010 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 55, no 4, 1038-1043 p.Article in journal (Refereed) Published
Abstract [en]

Balanced truncation is a standard method for model reduction, possessing many desirable properties such as preservation of model stability and a priori error bounds. Balanced truncation is conducted using controllability and observability Gramians. Generalized Gramians can be found by solving a set of linear matrix inequalities. In this paper, we show that these linear matrix inequalities can be extended so that the number of decision variables are at least doubled, leading to the concept of extended Gramians. Herein it is shown that the desirable properties of balanced truncation also hold with extended Gramians. The extended Gramians are especially useful for improving error bounds and for models possessing additional structural constraints, as is demonstrated by means of examples herein.

Place, publisher, year, edition, pages
IEEE , 2010. Vol. 55, no 4, 1038-1043 p.
Keyword [en]
Error bounds, linear matrix inequalities (LMIs), model order reduction, structure constraints, discrete-time-systems, uncertain systems, linear-systems
National Category
Electrical Engineering, Electronic Engineering, Information Engineering Control Engineering
URN: urn:nbn:se:kth:diva-19369DOI: 10.1109/tac.2010.2041984ISI: 000276251300029ScopusID: 2-s2.0-77950853364OAI: diva2:337416
Swedish Research Council, 2007-6350Swedish Research Council, 2009-4565
© 2010 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. QC 20100525 QC 20111110Available from: 2012-02-09 Created: 2010-08-05 Last updated: 2012-02-09Bibliographically approved

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