Examples on Stability for Infinite-Dimensional Systems

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    Abstract

    By means of examples, we study stability of infinite-dimensional linear and nonlinear systems. First we show that having a (strict) Lyapunov function does not imply asymptotic stability, even not for linear systems. Second, we show that to conclude (local) exponential stability from the linearization, care must be taken how the linearization is obtained.
    Original languageEnglish
    Title of host publicationMathematical Control Theory I
    EditorsM. Kanat Camlibel, R.P. Ramkrishna Pasumarthy, A. Agung Julius, Jacquelien M.A. Scherpen
    Place of PublicationLondon
    PublisherSpringer
    Pages343-348
    Number of pages6
    ISBN (Print)978-3-319-20987-6
    DOIs
    Publication statusPublished - 14 Jul 2015

    Publication series

    NameLecture Notes in Control and Information Sciences
    PublisherSpringer Verlag
    Number461
    Volume461
    ISSN (Print)0170-8643

    Keywords

    • MSC-53C38
    • MSC-34H05
    • METIS-314962
    • IR-98399
    • EWI-26283

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  • Cite this

    Zwart, H. J. (2015). Examples on Stability for Infinite-Dimensional Systems. In M. Kanat Camlibel, R. P. Ramkrishna Pasumarthy, A. Agung Julius, & J. M. A. Scherpen (Eds.), Mathematical Control Theory I (pp. 343-348). (Lecture Notes in Control and Information Sciences; Vol. 461, No. 461). London: Springer. https://doi.org/10.1007/978-3-319-20988-3_18