When does the H∞ fixed-lag smoothing saturate for finite smoothing lag

Leonid Mirkin, Gjerrit Meinsma

    Research output: Contribution to journalArticleAcademicpeer-review

    11 Citations (Scopus)


    A notable difference between the H∞ 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∞ performance saturates only if the H∞ 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 languageEnglish
    Pages (from-to)131-134
    Number of pages4
    JournalIEEE transactions on automatic control
    Issue number1
    Publication statusPublished - 2004


    • Mathematics
    • Delay estimation
    • Frequency
    • Mechanical engineering
    • Riccati equations
    • IR-101801
    • Signal processing
    • Sufficient conditions
    • Smoothing methods
    • Numerical simulation
    • METIS-219851
    • Signal generators

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