Stability of perturbed linear distributed parameter systems

L. Pandolfi, Heiko J. Zwart

    Research output: Contribution to journalArticleAcademicpeer-review

    5 Citations (Scopus)
    56 Downloads (Pure)

    Abstract

    We present an estimate for a class of unbounded perturbations of the generator of an exponentially stable semigroup. When this estimate is satisfied then the perturbed operator still generates an exponentially stable semigroup. For generators of holomorhic semigroups the class of allowed perturbations contains unbounded operators of the form HA¿, with . The estimate is given in terms of the norm of the solution of the Lyapunov equation which corresponds to the unperturbed system.
    Original languageUndefined
    Pages (from-to)257-264
    Number of pages8
    JournalSystems and control letters
    Volume17
    Issue number4
    DOIs
    Publication statusPublished - 1991

    Keywords

    • IR-29954
    • METIS-140588

    Cite this

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    title = "Stability of perturbed linear distributed parameter systems",
    abstract = "We present an estimate for a class of unbounded perturbations of the generator of an exponentially stable semigroup. When this estimate is satisfied then the perturbed operator still generates an exponentially stable semigroup. For generators of holomorhic semigroups the class of allowed perturbations contains unbounded operators of the form HA¿, with . The estimate is given in terms of the norm of the solution of the Lyapunov equation which corresponds to the unperturbed system.",
    keywords = "IR-29954, METIS-140588",
    author = "L. Pandolfi and Zwart, {Heiko J.}",
    year = "1991",
    doi = "10.1016/0167-6911(91)90141-Z",
    language = "Undefined",
    volume = "17",
    pages = "257--264",
    journal = "Systems and control letters",
    issn = "0167-6911",
    publisher = "Elsevier",
    number = "4",

    }

    Stability of perturbed linear distributed parameter systems. / Pandolfi, L.; Zwart, Heiko J.

    In: Systems and control letters, Vol. 17, No. 4, 1991, p. 257-264.

    Research output: Contribution to journalArticleAcademicpeer-review

    TY - JOUR

    T1 - Stability of perturbed linear distributed parameter systems

    AU - Pandolfi, L.

    AU - Zwart, Heiko J.

    PY - 1991

    Y1 - 1991

    N2 - We present an estimate for a class of unbounded perturbations of the generator of an exponentially stable semigroup. When this estimate is satisfied then the perturbed operator still generates an exponentially stable semigroup. For generators of holomorhic semigroups the class of allowed perturbations contains unbounded operators of the form HA¿, with . The estimate is given in terms of the norm of the solution of the Lyapunov equation which corresponds to the unperturbed system.

    AB - We present an estimate for a class of unbounded perturbations of the generator of an exponentially stable semigroup. When this estimate is satisfied then the perturbed operator still generates an exponentially stable semigroup. For generators of holomorhic semigroups the class of allowed perturbations contains unbounded operators of the form HA¿, with . The estimate is given in terms of the norm of the solution of the Lyapunov equation which corresponds to the unperturbed system.

    KW - IR-29954

    KW - METIS-140588

    U2 - 10.1016/0167-6911(91)90141-Z

    DO - 10.1016/0167-6911(91)90141-Z

    M3 - Article

    VL - 17

    SP - 257

    EP - 264

    JO - Systems and control letters

    JF - Systems and control letters

    SN - 0167-6911

    IS - 4

    ER -