From Lipschitzian to non-Lipschitzian characteristics : continuity of behaviors

M.K. Camlibel; M.K.K. Cevik; W.P.M.H. Heemels

doi:10.1109/CDC.2001.914593

From Lipschitzian to non-Lipschitzian characteristics : continuity of behaviors

M.K. Camlibel, M.K.K. Cevik, W.P.M.H. Heemels

Control Systems

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

6 Citations (Scopus)

Abstract

Linear complementarity systems are used to model discontinuous dynamical systems such as networks with ideal diodes and mechanical systems with unilateral constraints. In these systems mode changes are modeled by a relation between nonnegative, complementarity variables. We consider approximating systems obtained by replacing this non-Lipschitzian relation with a Lipschitzian function and investigate the convergence of the solutions of the approximating system to those of the ideal system as the Lipschitzian characteristic approaches to the (non-Lipschitzian) complementarity relation. It is shown that this kind of convergence holds for linear passive complementarity systems for which solutions are known to exist and to be unique. Moreover, this result is extended to systems that can be made passive by pole shifting

Original language	English
Title of host publication	Proceedings of the 39th IEEE conference on decision and control, Sydney, Australia, December 2000, vol. 5
Place of Publication	Piscataway
Publisher	Institute of Electrical and Electronics Engineers
Pages	4373-4378
ISBN (Print)	0-7803-6638-7
DOIs	https://doi.org/10.1109/CDC.2001.914593
Publication status	Published - 2000
Event	39th IEEE Conference on Decision and Control (CDC 2000) - Sydney, Australia Duration: 12 Dec 2000 → 15 Dec 2000

Conference

Conference	39th IEEE Conference on Decision and Control (CDC 2000)
Abbreviated title	CDC 2000
Country/Territory	Australia
City	Sydney
Period	12/12/00 → 15/12/00
Other

Access to Document

10.1109/CDC.2001.914593

Cite this

@inproceedings{1ad8728edafa4d00a7041291a9969350,

title = "From Lipschitzian to non-Lipschitzian characteristics : continuity of behaviors",

abstract = "Linear complementarity systems are used to model discontinuous dynamical systems such as networks with ideal diodes and mechanical systems with unilateral constraints. In these systems mode changes are modeled by a relation between nonnegative, complementarity variables. We consider approximating systems obtained by replacing this non-Lipschitzian relation with a Lipschitzian function and investigate the convergence of the solutions of the approximating system to those of the ideal system as the Lipschitzian characteristic approaches to the (non-Lipschitzian) complementarity relation. It is shown that this kind of convergence holds for linear passive complementarity systems for which solutions are known to exist and to be unique. Moreover, this result is extended to systems that can be made passive by pole shifting",

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

year = "2000",

doi = "10.1109/CDC.2001.914593",

language = "English",

isbn = "0-7803-6638-7",

pages = "4373--4378",

booktitle = "Proceedings of the 39th IEEE conference on decision and control, Sydney, Australia, December 2000, vol. 5",

publisher = "Institute of Electrical and Electronics Engineers",

address = "United States",

note = "39th IEEE Conference on Decision and Control (CDC 2000), CDC 2000 ; Conference date: 12-12-2000 Through 15-12-2000",

}

Camlibel, MK, Cevik, MKK & Heemels, WPMH 2000, From Lipschitzian to non-Lipschitzian characteristics : continuity of behaviors. in Proceedings of the 39th IEEE conference on decision and control, Sydney, Australia, December 2000, vol. 5. Institute of Electrical and Electronics Engineers, Piscataway, pp. 4373-4378, 39th IEEE Conference on Decision and Control (CDC 2000), Sydney, Australia, 12/12/00. https://doi.org/10.1109/CDC.2001.914593

From Lipschitzian to non-Lipschitzian characteristics : continuity of behaviors. / Camlibel, M.K.; Cevik, M.K.K.; Heemels, W.P.M.H.
Proceedings of the 39th IEEE conference on decision and control, Sydney, Australia, December 2000, vol. 5. Piscataway: Institute of Electrical and Electronics Engineers, 2000. p. 4373-4378.

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

TY - GEN

T1 - From Lipschitzian to non-Lipschitzian characteristics : continuity of behaviors

AU - Camlibel, M.K.

AU - Cevik, M.K.K.

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

PY - 2000

Y1 - 2000

N2 - Linear complementarity systems are used to model discontinuous dynamical systems such as networks with ideal diodes and mechanical systems with unilateral constraints. In these systems mode changes are modeled by a relation between nonnegative, complementarity variables. We consider approximating systems obtained by replacing this non-Lipschitzian relation with a Lipschitzian function and investigate the convergence of the solutions of the approximating system to those of the ideal system as the Lipschitzian characteristic approaches to the (non-Lipschitzian) complementarity relation. It is shown that this kind of convergence holds for linear passive complementarity systems for which solutions are known to exist and to be unique. Moreover, this result is extended to systems that can be made passive by pole shifting

AB - Linear complementarity systems are used to model discontinuous dynamical systems such as networks with ideal diodes and mechanical systems with unilateral constraints. In these systems mode changes are modeled by a relation between nonnegative, complementarity variables. We consider approximating systems obtained by replacing this non-Lipschitzian relation with a Lipschitzian function and investigate the convergence of the solutions of the approximating system to those of the ideal system as the Lipschitzian characteristic approaches to the (non-Lipschitzian) complementarity relation. It is shown that this kind of convergence holds for linear passive complementarity systems for which solutions are known to exist and to be unique. Moreover, this result is extended to systems that can be made passive by pole shifting

U2 - 10.1109/CDC.2001.914593

DO - 10.1109/CDC.2001.914593

M3 - Conference contribution

SN - 0-7803-6638-7

SP - 4373

EP - 4378

BT - Proceedings of the 39th IEEE conference on decision and control, Sydney, Australia, December 2000, vol. 5

PB - Institute of Electrical and Electronics Engineers

CY - Piscataway

T2 - 39th IEEE Conference on Decision and Control (CDC 2000)

Y2 - 12 December 2000 through 15 December 2000

ER -

From Lipschitzian to non-Lipschitzian characteristics : continuity of behaviors

Abstract

Conference

Access to Document

Fingerprint

Cite this