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).
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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