Modelling, well-posedness, and stability of switched electrical networks

W.P.M.H. Heemels, Arjan van der Schaft, J.M. Schumacher, M.K. Camlıbel

    Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

    23 Citations (Scopus)

    Abstract

    A modeling framework is proposed for circuits that are subject to both time and state events. The framework applies to switched networks with linear and piecewise linear elements including diodes and switches. We show that the linear complementarity formulation, which already has proved effective for piecewise linear networks, can be extended in a natural way to cover also switching circuits. We show that the proposed framework is sound in the sense that existence and uniqueness of solutions is guaranteed under a passivity assumption. We prove that only first-order impulses occur and characterize all situations that give rise to a state jump; moreover, we provide rules that determine the jump. Finally, we derive a stability result. Hence, for a subclass of hybrid dynamical systems, the issues of well-posedness, regularity of trajectories, jump rules, consistent states and stability are resolved.
    Original languageEnglish
    Title of host publicationHybrid Systems: Computation and Control
    Subtitle of host publication6th International Workshop, HSCC 2003 Prague, Czech Republic, April 3–5, 2003 Proceedings
    EditorsOded Maler, Amir Pnueli
    Place of PublicationBerlin, Germany
    PublisherSpringer
    Pages249-266
    ISBN (Electronic)978-3-540-36580-8
    ISBN (Print)978-3-540-00913-9
    DOIs
    Publication statusPublished - 2003
    Event6th International Workshop on Hybrid Systems: Computation and Control, HSCC 2003 - Prague, Czech Republic
    Duration: 3 Apr 20035 Apr 2003
    Conference number: 6

    Publication series

    NameLecture Notes in Computer Science
    PublisherSpringer
    Volume2623
    ISSN (Print)0302-9743

    Conference

    Conference6th International Workshop on Hybrid Systems: Computation and Control, HSCC 2003
    Abbreviated titleHSCC
    CountryCzech Republic
    CityPrague
    Period3/04/035/04/03

    Fingerprint

    Linear networks
    Switching circuits
    Switching networks
    Dynamical systems
    Diodes
    Switches
    Trajectories
    Acoustic waves
    Networks (circuits)

    Keywords

    • IR-85673

    Cite this

    Heemels, W. P. M. H., van der Schaft, A., Schumacher, J. M., & Camlıbel, M. K. (2003). Modelling, well-posedness, and stability of switched electrical networks. In O. Maler, & A. Pnueli (Eds.), Hybrid Systems: Computation and Control: 6th International Workshop, HSCC 2003 Prague, Czech Republic, April 3–5, 2003 Proceedings (pp. 249-266). (Lecture Notes in Computer Science; Vol. 2623). Berlin, Germany: Springer. https://doi.org/10.1007/3-540-36580-X_20
    Heemels, W.P.M.H. ; van der Schaft, Arjan ; Schumacher, J.M. ; Camlıbel, M.K. / Modelling, well-posedness, and stability of switched electrical networks. Hybrid Systems: Computation and Control: 6th International Workshop, HSCC 2003 Prague, Czech Republic, April 3–5, 2003 Proceedings. editor / Oded Maler ; Amir Pnueli. Berlin, Germany : Springer, 2003. pp. 249-266 (Lecture Notes in Computer Science).
    @inbook{86d4bb14f7c0482286c78a9154008f04,
    title = "Modelling, well-posedness, and stability of switched electrical networks",
    abstract = "A modeling framework is proposed for circuits that are subject to both time and state events. The framework applies to switched networks with linear and piecewise linear elements including diodes and switches. We show that the linear complementarity formulation, which already has proved effective for piecewise linear networks, can be extended in a natural way to cover also switching circuits. We show that the proposed framework is sound in the sense that existence and uniqueness of solutions is guaranteed under a passivity assumption. We prove that only first-order impulses occur and characterize all situations that give rise to a state jump; moreover, we provide rules that determine the jump. Finally, we derive a stability result. Hence, for a subclass of hybrid dynamical systems, the issues of well-posedness, regularity of trajectories, jump rules, consistent states and stability are resolved.",
    keywords = "IR-85673",
    author = "W.P.M.H. Heemels and {van der Schaft}, Arjan and J.M. Schumacher and M.K. Camlıbel",
    year = "2003",
    doi = "10.1007/3-540-36580-X_20",
    language = "English",
    isbn = "978-3-540-00913-9",
    series = "Lecture Notes in Computer Science",
    publisher = "Springer",
    pages = "249--266",
    editor = "Oded Maler and Amir Pnueli",
    booktitle = "Hybrid Systems: Computation and Control",

    }

    Heemels, WPMH, van der Schaft, A, Schumacher, JM & Camlıbel, MK 2003, Modelling, well-posedness, and stability of switched electrical networks. in O Maler & A Pnueli (eds), Hybrid Systems: Computation and Control: 6th International Workshop, HSCC 2003 Prague, Czech Republic, April 3–5, 2003 Proceedings. Lecture Notes in Computer Science, vol. 2623, Springer, Berlin, Germany, pp. 249-266, 6th International Workshop on Hybrid Systems: Computation and Control, HSCC 2003, Prague, Czech Republic, 3/04/03. https://doi.org/10.1007/3-540-36580-X_20

    Modelling, well-posedness, and stability of switched electrical networks. / Heemels, W.P.M.H.; van der Schaft, Arjan; Schumacher, J.M.; Camlıbel, M.K.

    Hybrid Systems: Computation and Control: 6th International Workshop, HSCC 2003 Prague, Czech Republic, April 3–5, 2003 Proceedings. ed. / Oded Maler; Amir Pnueli. Berlin, Germany : Springer, 2003. p. 249-266 (Lecture Notes in Computer Science; Vol. 2623).

    Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

    TY - CHAP

    T1 - Modelling, well-posedness, and stability of switched electrical networks

    AU - Heemels, W.P.M.H.

    AU - van der Schaft, Arjan

    AU - Schumacher, J.M.

    AU - Camlıbel, M.K.

    PY - 2003

    Y1 - 2003

    N2 - A modeling framework is proposed for circuits that are subject to both time and state events. The framework applies to switched networks with linear and piecewise linear elements including diodes and switches. We show that the linear complementarity formulation, which already has proved effective for piecewise linear networks, can be extended in a natural way to cover also switching circuits. We show that the proposed framework is sound in the sense that existence and uniqueness of solutions is guaranteed under a passivity assumption. We prove that only first-order impulses occur and characterize all situations that give rise to a state jump; moreover, we provide rules that determine the jump. Finally, we derive a stability result. Hence, for a subclass of hybrid dynamical systems, the issues of well-posedness, regularity of trajectories, jump rules, consistent states and stability are resolved.

    AB - A modeling framework is proposed for circuits that are subject to both time and state events. The framework applies to switched networks with linear and piecewise linear elements including diodes and switches. We show that the linear complementarity formulation, which already has proved effective for piecewise linear networks, can be extended in a natural way to cover also switching circuits. We show that the proposed framework is sound in the sense that existence and uniqueness of solutions is guaranteed under a passivity assumption. We prove that only first-order impulses occur and characterize all situations that give rise to a state jump; moreover, we provide rules that determine the jump. Finally, we derive a stability result. Hence, for a subclass of hybrid dynamical systems, the issues of well-posedness, regularity of trajectories, jump rules, consistent states and stability are resolved.

    KW - IR-85673

    U2 - 10.1007/3-540-36580-X_20

    DO - 10.1007/3-540-36580-X_20

    M3 - Chapter

    SN - 978-3-540-00913-9

    T3 - Lecture Notes in Computer Science

    SP - 249

    EP - 266

    BT - Hybrid Systems: Computation and Control

    A2 - Maler, Oded

    A2 - Pnueli, Amir

    PB - Springer

    CY - Berlin, Germany

    ER -

    Heemels WPMH, van der Schaft A, Schumacher JM, Camlıbel MK. Modelling, well-posedness, and stability of switched electrical networks. In Maler O, Pnueli A, editors, Hybrid Systems: Computation and Control: 6th International Workshop, HSCC 2003 Prague, Czech Republic, April 3–5, 2003 Proceedings. Berlin, Germany: Springer. 2003. p. 249-266. (Lecture Notes in Computer Science). https://doi.org/10.1007/3-540-36580-X_20