Gain perturbation tolerance in H state feedback control

Masayuki Fujita, Kenko Uchida, Fumio Matsumura

    Research output: Contribution to journalArticle

    6 Citations (Scopus)

    Abstract

    The gain perturbation tolerance property of H-optimal state feedback (HISF) systems is considered. The following two problems are discussed: (1) for what gain perturbations would the perturbed closed-loop system remain stable? (2) for what gain perturbations would the perturbed closed-loop transfer function satisfy the specified H-norm performance? In each case we establish general sufficient conditions in the frequency domain. In particular, under a certain orthogonality condition, the HISF systems are shown to possess an infinite gain increase tolerance for stability. The result obtained also provides insight into the gain reduction tolerance problem. Furthermore, we show that, under certain conditions, the specified H-norm performance of the HISF systems is preserved even with an infinite gain increase. Concerning closed-loop performance robustness against gain perturbations, we see remarkable differences between the case where controlled outputs include a direct transmission of controls and the case where they do not.

    Original languageEnglish
    Pages (from-to)315-328
    Number of pages14
    JournalInternational Journal of Control
    Volume51
    Issue number2
    Publication statusPublished - 1990 Feb

    Fingerprint

    State feedback
    Feedback control
    Closed loop systems
    Transfer functions

    ASJC Scopus subject areas

    • Control and Systems Engineering

    Cite this

    Gain perturbation tolerance in H state feedback control. / Fujita, Masayuki; Uchida, Kenko; Matsumura, Fumio.

    In: International Journal of Control, Vol. 51, No. 2, 02.1990, p. 315-328.

    Research output: Contribution to journalArticle

    Fujita, Masayuki ; Uchida, Kenko ; Matsumura, Fumio. / Gain perturbation tolerance in H state feedback control. In: International Journal of Control. 1990 ; Vol. 51, No. 2. pp. 315-328.
    @article{a7347fdb08f54fd294e017404f80c1e1,
    title = "Gain perturbation tolerance in H∞ state feedback control",
    abstract = "The gain perturbation tolerance property of H∞-optimal state feedback (HISF) systems is considered. The following two problems are discussed: (1) for what gain perturbations would the perturbed closed-loop system remain stable? (2) for what gain perturbations would the perturbed closed-loop transfer function satisfy the specified H∞-norm performance? In each case we establish general sufficient conditions in the frequency domain. In particular, under a certain orthogonality condition, the HISF systems are shown to possess an infinite gain increase tolerance for stability. The result obtained also provides insight into the gain reduction tolerance problem. Furthermore, we show that, under certain conditions, the specified H∞-norm performance of the HISF systems is preserved even with an infinite gain increase. Concerning closed-loop performance robustness against gain perturbations, we see remarkable differences between the case where controlled outputs include a direct transmission of controls and the case where they do not.",
    author = "Masayuki Fujita and Kenko Uchida and Fumio Matsumura",
    year = "1990",
    month = "2",
    language = "English",
    volume = "51",
    pages = "315--328",
    journal = "International Journal of Control",
    issn = "0020-7179",
    publisher = "Taylor and Francis Ltd.",
    number = "2",

    }

    TY - JOUR

    T1 - Gain perturbation tolerance in H∞ state feedback control

    AU - Fujita, Masayuki

    AU - Uchida, Kenko

    AU - Matsumura, Fumio

    PY - 1990/2

    Y1 - 1990/2

    N2 - The gain perturbation tolerance property of H∞-optimal state feedback (HISF) systems is considered. The following two problems are discussed: (1) for what gain perturbations would the perturbed closed-loop system remain stable? (2) for what gain perturbations would the perturbed closed-loop transfer function satisfy the specified H∞-norm performance? In each case we establish general sufficient conditions in the frequency domain. In particular, under a certain orthogonality condition, the HISF systems are shown to possess an infinite gain increase tolerance for stability. The result obtained also provides insight into the gain reduction tolerance problem. Furthermore, we show that, under certain conditions, the specified H∞-norm performance of the HISF systems is preserved even with an infinite gain increase. Concerning closed-loop performance robustness against gain perturbations, we see remarkable differences between the case where controlled outputs include a direct transmission of controls and the case where they do not.

    AB - The gain perturbation tolerance property of H∞-optimal state feedback (HISF) systems is considered. The following two problems are discussed: (1) for what gain perturbations would the perturbed closed-loop system remain stable? (2) for what gain perturbations would the perturbed closed-loop transfer function satisfy the specified H∞-norm performance? In each case we establish general sufficient conditions in the frequency domain. In particular, under a certain orthogonality condition, the HISF systems are shown to possess an infinite gain increase tolerance for stability. The result obtained also provides insight into the gain reduction tolerance problem. Furthermore, we show that, under certain conditions, the specified H∞-norm performance of the HISF systems is preserved even with an infinite gain increase. Concerning closed-loop performance robustness against gain perturbations, we see remarkable differences between the case where controlled outputs include a direct transmission of controls and the case where they do not.

    UR - http://www.scopus.com/inward/record.url?scp=0025386433&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=0025386433&partnerID=8YFLogxK

    M3 - Article

    AN - SCOPUS:0025386433

    VL - 51

    SP - 315

    EP - 328

    JO - International Journal of Control

    JF - International Journal of Control

    SN - 0020-7179

    IS - 2

    ER -