The nature of solutions to linear passive complementarity systems

M.K. Camlibel; W.P.M.H. Heemels; J.M. Schumacher

doi:10.1109/CDC.1999.831401

The nature of solutions to linear passive complementarity systems

M.K. Camlibel
, W.P.M.H. Heemels
, J.M. Schumacher

Control Systems

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

205 Downloads (Pure)

Abstract

Linear passive systems with complementarity conditions (as an application, one may consider linear passive networks with ideal diodes) are studied. For these systems contained in the linear complementarity class of hybrid systems, existence and uniqueness of solutions are established. Moreover, the nature of the solutions is characterized. In particular, it is shown that derivatives of Dirac impulses cannot occur and Dirac impulses and jumps in the state variable can only occur at t=0. These facts reduce the `complexity' of the solution in a sense. Finally, we give an explicit characterization of the set of initial states from which no Dirac impulses or discontinuities in the state variable occur. This set of `regular states' turns out to be invariant under the dynamics

Original language	English
Title of host publication	Proceedings 38th IEEE Conference on Decision and Control, December 7-10, 1999, Phoenix AZ, USA
Place of Publication	Piscataway
Publisher	Institute of Electrical and Electronics Engineers
Pages	3043-3048
ISBN (Print)	0-7803-5250-5
DOIs	https://doi.org/10.1109/CDC.1999.831401
Publication status	Published - 1999
Event	38th IEEE Conference on Decision and Control (CDC 1999) - Phoenix, United States Duration: 7 Dec 1999 → 10 Dec 1999 Conference number: 38

Conference

Conference	38th IEEE Conference on Decision and Control (CDC 1999)
Abbreviated title	CDC 1999
Country/Territory	United States
City	Phoenix
Period	7/12/99 → 10/12/99

Access to Document

10.1109/CDC.1999.831401

publishers versionFinal published version, 588 KB

Cite this

@inproceedings{f217991cedc0445793b79a0e81f6bd14,

title = "The nature of solutions to linear passive complementarity systems",

abstract = "Linear passive systems with complementarity conditions (as an application, one may consider linear passive networks with ideal diodes) are studied. For these systems contained in the linear complementarity class of hybrid systems, existence and uniqueness of solutions are established. Moreover, the nature of the solutions is characterized. In particular, it is shown that derivatives of Dirac impulses cannot occur and Dirac impulses and jumps in the state variable can only occur at t=0. These facts reduce the `complexity' of the solution in a sense. Finally, we give an explicit characterization of the set of initial states from which no Dirac impulses or discontinuities in the state variable occur. This set of `regular states' turns out to be invariant under the dynamics",

author = "M.K. Camlibel and W.P.M.H. Heemels and J.M. Schumacher",

year = "1999",

doi = "10.1109/CDC.1999.831401",

language = "English",

isbn = "0-7803-5250-5",

pages = "3043--3048",

booktitle = "Proceedings 38th IEEE Conference on Decision and Control, December 7-10, 1999, Phoenix AZ, USA",

publisher = "Institute of Electrical and Electronics Engineers",

address = "United States",

note = "38th IEEE Conference on Decision and Control (CDC 1999), CDC 1999 ; Conference date: 07-12-1999 Through 10-12-1999",

}

Camlibel, MK, Heemels, WPMH & Schumacher, JM 1999, The nature of solutions to linear passive complementarity systems. in Proceedings 38th IEEE Conference on Decision and Control, December 7-10, 1999, Phoenix AZ, USA. Institute of Electrical and Electronics Engineers, Piscataway, pp. 3043-3048, 38th IEEE Conference on Decision and Control (CDC 1999), Phoenix, Arizona, United States, 7/12/99. https://doi.org/10.1109/CDC.1999.831401

The nature of solutions to linear passive complementarity systems. / Camlibel, M.K.; Heemels, W.P.M.H.; Schumacher, J.M.
Proceedings 38th IEEE Conference on Decision and Control, December 7-10, 1999, Phoenix AZ, USA. Piscataway: Institute of Electrical and Electronics Engineers, 1999. p. 3043-3048.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - The nature of solutions to linear passive complementarity systems

AU - Camlibel, M.K.

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

AU - Schumacher, J.M.

N1 - Conference code: 38

PY - 1999

Y1 - 1999

N2 - Linear passive systems with complementarity conditions (as an application, one may consider linear passive networks with ideal diodes) are studied. For these systems contained in the linear complementarity class of hybrid systems, existence and uniqueness of solutions are established. Moreover, the nature of the solutions is characterized. In particular, it is shown that derivatives of Dirac impulses cannot occur and Dirac impulses and jumps in the state variable can only occur at t=0. These facts reduce the `complexity' of the solution in a sense. Finally, we give an explicit characterization of the set of initial states from which no Dirac impulses or discontinuities in the state variable occur. This set of `regular states' turns out to be invariant under the dynamics

AB - Linear passive systems with complementarity conditions (as an application, one may consider linear passive networks with ideal diodes) are studied. For these systems contained in the linear complementarity class of hybrid systems, existence and uniqueness of solutions are established. Moreover, the nature of the solutions is characterized. In particular, it is shown that derivatives of Dirac impulses cannot occur and Dirac impulses and jumps in the state variable can only occur at t=0. These facts reduce the `complexity' of the solution in a sense. Finally, we give an explicit characterization of the set of initial states from which no Dirac impulses or discontinuities in the state variable occur. This set of `regular states' turns out to be invariant under the dynamics

U2 - 10.1109/CDC.1999.831401

DO - 10.1109/CDC.1999.831401

M3 - Conference contribution

SN - 0-7803-5250-5

SP - 3043

EP - 3048

BT - Proceedings 38th IEEE Conference on Decision and Control, December 7-10, 1999, Phoenix AZ, USA

PB - Institute of Electrical and Electronics Engineers

CY - Piscataway

T2 - 38th IEEE Conference on Decision and Control (CDC 1999)

Y2 - 7 December 1999 through 10 December 1999

ER -

The nature of solutions to linear passive complementarity systems

Abstract

Conference

Access to Document

Fingerprint

Cite this