On frequency weighted balanced truncation: A constructive counterexample to Enns' conjecture

Tony Van Gestel, Bart De Moor, Brian D.O. Anderson, Peter Van Overschee

    Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

    1 Citation (Scopus)

    Abstract

    The concept of frequency weighted balancing, as proposed by Enns, is a generalization of internally balanced model truncation. Internally balanced truncation is simple to apply and additionally attractive because of the existence of an upper -ffœ error bound that is a function of the neglected Hankel singular values. A conjecture on the generalization of this upper error bound for the case of frequency weighted balanced truncation was formulated by Enns, but the proof has not been found. In this paper, Enns' conjecture is refuted and it is shown that there does not exist a frequency weighted upper error bound that depends only on neglected frequency weighted Hankel singular values. It is explained that this is due to cross terms which appear in the frequency weighted error bound. However, these cross terms are inherent in the frequency weighted balancing technique proposed by Enns.

    Original languageEnglish
    Title of host publication2001 European Control Conference, ECC 2001
    PublisherInstitute of Electrical and Electronics Engineers Inc.
    Pages2493-2498
    Number of pages6
    ISBN (Electronic)9783952417362
    DOIs
    Publication statusPublished - 2001
    Event6th European Control Conference, ECC 2001 - Porto, Portugal
    Duration: 4 Sept 20017 Sept 2001

    Publication series

    Name2001 European Control Conference, ECC 2001

    Conference

    Conference6th European Control Conference, ECC 2001
    Country/TerritoryPortugal
    CityPorto
    Period4/09/017/09/01

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