On multiple-delay approximations of multiple-derivative controllers

Yan Wan, Sandip Roy, Antonie Arij Stoorvogel, Ali Saberi

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    We study approximation of multiple-derivative output feedback for linear time-invariant (LTI) plants using multiple-delay approximations. We obtain a condition on the plant and feedback that yields an equivalence between the closed-loop spectra for the approximate feedbacks and the desired multiple-derivative feedbacks. On the other hand, we use a scalar example to illustrate that multiple-delay approximations of sufficiently high derivatives may in some cases yield closed-loop spectra that differ greatly from the dynamics upon derivative feedback (for instance, containing many and very large right half plane poles), while in other cases replicating the derivative feedback perfectly. Finally, through understanding this dichotomy, we present a condition for stabilizing a SISO relative degree-1 plant when a delay implementation of the first-order derivative is used in the output feedback control law.
    Original languageUndefined
    Title of host publicationEuropean Control Conference
    PublisherEuropean Union Control Association
    Number of pages6
    ISBN (Print)978-963-311-369-1
    Publication statusPublished - Aug 2009
    Event2009 European Control Conference, ECC 2009 - Budapest, Hungary
    Duration: 23 Aug 200926 Aug 2009

    Publication series

    PublisherEuropean Union Control Association


    Conference2009 European Control Conference, ECC 2009
    Abbreviated titleECC


    • METIS-263970
    • EWI-15877
    • IR-67843

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