Further results on saturated globally stabilizing linear state feedback control laws for single-input neutrally stable planar systems

Tao Yang, Antonie Arij Stoorvogel, Ali Saberi, Karl H. Johansson

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

    2 Citations (Scopus)

    Abstract

    It is known that for single-input neutrally stable planar systems, there exists a class of saturated globally stabilizing linear state feedback control laws. The goal of this paper is to characterize the dynamic behavior for such a system under arbitrary locally stabilizing linear state feedback control laws. On the one hand, for the continuous-time case, we show that all locally stabilizing linear state feedback control laws are also globally stabilizing control laws. On the other hand, for the discrete-time case, we first show that this property does not hold by explicitly constructing nontrivial periodic solution for a particular system. We then show for an example that there exists more globally stabilizing linear state feedback control laws than well known ones in the literature.
    Original languageUndefined
    Title of host publicationProceedings of the European Control Conference 2013 (ECC13)
    PublisherOmniPress
    Pages2728-2733
    Number of pages6
    ISBN (Print)978-3-9524173-4-8
    Publication statusPublished - 2013
    Event2013 European Control Conference, ECC 2013 - Zürich, Switzerland
    Duration: 17 Jul 201319 Jul 2013

    Publication series

    Name
    PublisherOmnipress

    Conference

    Conference2013 European Control Conference, ECC 2013
    Abbreviated titleECC
    CountrySwitzerland
    CityZürich
    Period17/07/1319/07/13

    Keywords

    • EWI-23870
    • METIS-300109
    • IR-87576

    Cite this

    Yang, T., Stoorvogel, A. A., Saberi, A., & Johansson, K. H. (2013). Further results on saturated globally stabilizing linear state feedback control laws for single-input neutrally stable planar systems. In Proceedings of the European Control Conference 2013 (ECC13) (pp. 2728-2733). OmniPress.
    Yang, Tao ; Stoorvogel, Antonie Arij ; Saberi, Ali ; Johansson, Karl H. / Further results on saturated globally stabilizing linear state feedback control laws for single-input neutrally stable planar systems. Proceedings of the European Control Conference 2013 (ECC13). OmniPress, 2013. pp. 2728-2733
    @inproceedings{5f1251eb7ce04ceaaf52040f96dae18d,
    title = "Further results on saturated globally stabilizing linear state feedback control laws for single-input neutrally stable planar systems",
    abstract = "It is known that for single-input neutrally stable planar systems, there exists a class of saturated globally stabilizing linear state feedback control laws. The goal of this paper is to characterize the dynamic behavior for such a system under arbitrary locally stabilizing linear state feedback control laws. On the one hand, for the continuous-time case, we show that all locally stabilizing linear state feedback control laws are also globally stabilizing control laws. On the other hand, for the discrete-time case, we first show that this property does not hold by explicitly constructing nontrivial periodic solution for a particular system. We then show for an example that there exists more globally stabilizing linear state feedback control laws than well known ones in the literature.",
    keywords = "EWI-23870, METIS-300109, IR-87576",
    author = "Tao Yang and Stoorvogel, {Antonie Arij} and Ali Saberi and Johansson, {Karl H.}",
    year = "2013",
    language = "Undefined",
    isbn = "978-3-9524173-4-8",
    publisher = "OmniPress",
    pages = "2728--2733",
    booktitle = "Proceedings of the European Control Conference 2013 (ECC13)",

    }

    Yang, T, Stoorvogel, AA, Saberi, A & Johansson, KH 2013, Further results on saturated globally stabilizing linear state feedback control laws for single-input neutrally stable planar systems. in Proceedings of the European Control Conference 2013 (ECC13). OmniPress, pp. 2728-2733, 2013 European Control Conference, ECC 2013, Zürich, Switzerland, 17/07/13.

    Further results on saturated globally stabilizing linear state feedback control laws for single-input neutrally stable planar systems. / Yang, Tao; Stoorvogel, Antonie Arij; Saberi, Ali; Johansson, Karl H.

    Proceedings of the European Control Conference 2013 (ECC13). OmniPress, 2013. p. 2728-2733.

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

    TY - GEN

    T1 - Further results on saturated globally stabilizing linear state feedback control laws for single-input neutrally stable planar systems

    AU - Yang, Tao

    AU - Stoorvogel, Antonie Arij

    AU - Saberi, Ali

    AU - Johansson, Karl H.

    PY - 2013

    Y1 - 2013

    N2 - It is known that for single-input neutrally stable planar systems, there exists a class of saturated globally stabilizing linear state feedback control laws. The goal of this paper is to characterize the dynamic behavior for such a system under arbitrary locally stabilizing linear state feedback control laws. On the one hand, for the continuous-time case, we show that all locally stabilizing linear state feedback control laws are also globally stabilizing control laws. On the other hand, for the discrete-time case, we first show that this property does not hold by explicitly constructing nontrivial periodic solution for a particular system. We then show for an example that there exists more globally stabilizing linear state feedback control laws than well known ones in the literature.

    AB - It is known that for single-input neutrally stable planar systems, there exists a class of saturated globally stabilizing linear state feedback control laws. The goal of this paper is to characterize the dynamic behavior for such a system under arbitrary locally stabilizing linear state feedback control laws. On the one hand, for the continuous-time case, we show that all locally stabilizing linear state feedback control laws are also globally stabilizing control laws. On the other hand, for the discrete-time case, we first show that this property does not hold by explicitly constructing nontrivial periodic solution for a particular system. We then show for an example that there exists more globally stabilizing linear state feedback control laws than well known ones in the literature.

    KW - EWI-23870

    KW - METIS-300109

    KW - IR-87576

    M3 - Conference contribution

    SN - 978-3-9524173-4-8

    SP - 2728

    EP - 2733

    BT - Proceedings of the European Control Conference 2013 (ECC13)

    PB - OmniPress

    ER -

    Yang T, Stoorvogel AA, Saberi A, Johansson KH. Further results on saturated globally stabilizing linear state feedback control laws for single-input neutrally stable planar systems. In Proceedings of the European Control Conference 2013 (ECC13). OmniPress. 2013. p. 2728-2733