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

W.P.M.H. Heemels, M.K. Camlibel, A.J. Schaft, van der, J.M. Schumacher

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

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 resolve
LanguageEnglish
Title of host publicationHybrid Systems: Computation and Control
EditorsO. Maler, A. Pnueli
PublisherSpringer
Pages249-266
Number of pages18
ISBN (Print)3-540-00913-2
StatePublished - 2003
Event6th International Workshop on Hybrid Systems: Computation and Control (HSCC 2003) - Prague, Czech Republic
Duration: 3 Mar 20035 Mar 2003
Conference number: 6

Publication series

NameLecture notes in computer science
Volume2623
ISSN (Print)0302-9743

Conference

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

Fingerprint

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

Cite this

Heemels, W. P. M. H., Camlibel, M. K., Schaft, van der, A. J., & Schumacher, J. M. (2003). Modelling, well-posedness, and stability of switched electrical networks. In O. Maler, & A. Pnueli (Eds.), Hybrid Systems: Computation and Control (pp. 249-266). (Lecture notes in computer science; Vol. 2623). Springer.
Heemels, W.P.M.H. ; Camlibel, M.K. ; Schaft, van der, A.J. ; Schumacher, J.M./ Modelling, well-posedness, and stability of switched electrical networks. Hybrid Systems: Computation and Control. editor / O. Maler ; A. Pnueli. Springer, 2003. pp. 249-266 (Lecture notes in computer science).
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Heemels, WPMH, Camlibel, MK, Schaft, van der, AJ & Schumacher, JM 2003, Modelling, well-posedness, and stability of switched electrical networks. in O Maler & A Pnueli (eds), Hybrid Systems: Computation and Control. Lecture notes in computer science, vol. 2623, Springer, pp. 249-266, 6th International Workshop on Hybrid Systems: Computation and Control (HSCC 2003), Prague, Czech Republic, 3/03/03.

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

Hybrid Systems: Computation and Control. ed. / O. Maler; A. Pnueli. Springer, 2003. p. 249-266 (Lecture notes in computer science; Vol. 2623).

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

TY - CHAP

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

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

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AU - Schaft, van der,A.J.

AU - Schumacher,J.M.

PY - 2003

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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 resolve

M3 - Chapter

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Heemels WPMH, Camlibel MK, Schaft, van der AJ, Schumacher JM. Modelling, well-posedness, and stability of switched electrical networks. In Maler O, Pnueli A, editors, Hybrid Systems: Computation and Control. Springer. 2003. p. 249-266. (Lecture notes in computer science).