When does the $H^\infty$ fixed-lag smoothing performance saturates?

Leonid Mirkin, Gjerrit Meinsma

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    Abstract

    A notable difference between the $H^2$ and $H^\infty$ smoothing is that the achievable performance in the latter problem might “saturate” as the function of the smoothing lag in the sense that there might exist a finite smoothing lag for which the achievable performance level is the same as for the infinite smoothing lag. In this note necessary and sufficient conditions under which such a saturation occurs are derived. In particular, it is shown that the $H^\infty$ performance saturates only if the $H^\infty$ norm of the optimal error system is achieved at the infinite frequency, i.e., if the worst case disturbance for the infinite smoothing lag case can be arbitrarily fast and thus in a sense unpredictable.
    Original languageUndefined
    Title of host publicationProceedings of the 15th IFAC World Congress
    Place of PublicationBarcelona, Spanje
    PublisherElsevier
    Pages121-124
    Number of pages4
    ISBN (Print)978-0-08-044295-2
    Publication statusPublished - 2002
    Event15th IFAC World Congress 2002 - Barcelona, Spain
    Duration: 21 Jul 200226 Jul 2002
    Conference number: 15
    http://folk.ntnu.no/skoge/prost/proceedings/ifac2002/home.htm

    Publication series

    Name
    PublisherElsevier

    Conference

    Conference15th IFAC World Congress 2002
    CountrySpain
    CityBarcelona
    Period21/07/0226/07/02
    Internet address

    Keywords

    • METIS-210619
    • Riccati equation
    • EWI-16738
    • $H_\infty$ estimation
    • Fixed-lag smoothing
    • IR-69139

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