Switched networks and complementarity

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

Research output: Contribution to journalArticleAcademicpeer-review

59 Citations (Scopus)
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Abstract

A modeling framework is proposed for circuits that are subject both to externally induced switches (time events) and to state events. The framework applies to switched networks with linear and piecewise-linear elements, including diodes. We show that the linear complementarity formulation, which already has proved effective for piecewise-linear networks, can be extended in a natural way to also cover switching circuits. To achieve this, we use a generalization of the linear complementarity problem known as the cone-complementarity problem. 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 show that within our framework, energy cannot increase as a result of a jump, and we derive a stability result from this.
Original languageUndefined
Article number10.1109/TCSI.2003.815195
Pages (from-to)1036-1046
Number of pages11
JournalIEEE transactions on circuits and systems I: fundamental theory and applications
Volume50
Issue number8
DOIs
Publication statusPublished - Aug 2003

Keywords

  • IR-69094
  • METIS-213209
  • Complementarity systems
  • EWI-16764
  • piecewise-linear systems
  • ideal switches
  • ideal diodes
  • Hybrid systems

Cite this

Camlıbel, M. K., Heemels, W. P. M. H., van der Schaft, A., & Schumacher, J. M. (2003). Switched networks and complementarity. IEEE transactions on circuits and systems I: fundamental theory and applications, 50(8), 1036-1046. [10.1109/TCSI.2003.815195]. https://doi.org/10.1109/TCSI.2003.815195
Camlıbel, M.K. ; Heemels, W.P.M.H. ; van der Schaft, Arjan ; Schumacher, J.M. / Switched networks and complementarity. In: IEEE transactions on circuits and systems I: fundamental theory and applications. 2003 ; Vol. 50, No. 8. pp. 1036-1046.
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abstract = "A modeling framework is proposed for circuits that are subject both to externally induced switches (time events) and to state events. The framework applies to switched networks with linear and piecewise-linear elements, including diodes. We show that the linear complementarity formulation, which already has proved effective for piecewise-linear networks, can be extended in a natural way to also cover switching circuits. To achieve this, we use a generalization of the linear complementarity problem known as the cone-complementarity problem. 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 show that within our framework, energy cannot increase as a result of a jump, and we derive a stability result from this.",
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Camlıbel, MK, Heemels, WPMH, van der Schaft, A & Schumacher, JM 2003, 'Switched networks and complementarity' IEEE transactions on circuits and systems I: fundamental theory and applications, vol. 50, no. 8, 10.1109/TCSI.2003.815195, pp. 1036-1046. https://doi.org/10.1109/TCSI.2003.815195

Switched networks and complementarity. / Camlıbel, M.K.; Heemels, W.P.M.H.; van der Schaft, Arjan; Schumacher, J.M.

In: IEEE transactions on circuits and systems I: fundamental theory and applications, Vol. 50, No. 8, 10.1109/TCSI.2003.815195, 08.2003, p. 1036-1046.

Research output: Contribution to journalArticleAcademicpeer-review

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Camlıbel MK, Heemels WPMH, van der Schaft A, Schumacher JM. Switched networks and complementarity. IEEE transactions on circuits and systems I: fundamental theory and applications. 2003 Aug;50(8):1036-1046. 10.1109/TCSI.2003.815195. https://doi.org/10.1109/TCSI.2003.815195