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

    Keywords

    • IR-85673

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  • 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