A semigroup approach to Port Hamiltonian systems associated with linear skew symmetric operator

Y. Le Gorrec; H. Zwart; B. Maschke

A semigroup approach to Port Hamiltonian systems associated with linear skew symmetric operator

Y. Le Gorrec, H. Zwart, B. Maschke

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

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Abstract

In this paper we first define a Dirac structure on a Hilbert spaces associated with a skew-symmetric linear operator including port variables on the boundary of its domain. Secondly, we associate $C_0$-semigroup with some parameterization of the boundary port variables and define a family of boundary control systems. Thirdly we define a linear port controlled Hamiltonian system associated with the previously defined Dirac structure and generated by a symmetric positive operator defining the energy of the system.

Original language	English
Title of host publication	Proceedings 16th International symposium on Mathematical Theory of Networks and Systems
Subtitle of host publication	Leuven, Belgium, July 5-9, 2004
Editors	Bart De Mor, Bart Motmans, Jan Willems, Paul Van Dooren, Vincent Blondel
Place of Publication	Leuven, Belgium
Publisher	Katholieke Universiteit Leuven
Number of pages	14
ISBN (Print)	90-5682-517-8
Publication status	Published - 2004
Event	16th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2004 - Leuven, Belgium Duration: 5 Jul 2004 → 9 Jul 2004 Conference number: 16

Conference

Conference	16th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2004
Abbreviated title	MTNS
Country/Territory	Belgium
City	Leuven
Period	5/07/04 → 9/07/04

Keywords

MSC-93C20

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Le Gorrec, Y., Zwart, H., & Maschke, B. (2004). A semigroup approach to Port Hamiltonian systems associated with linear skew symmetric operator. In B. De Mor, B. Motmans, J. Willems, P. Van Dooren, & V. Blondel (Eds.), Proceedings 16th International symposium on Mathematical Theory of Networks and Systems: Leuven, Belgium, July 5-9, 2004 Katholieke Universiteit Leuven.

Le Gorrec, Y. ; Zwart, H. ; Maschke, B. / A semigroup approach to Port Hamiltonian systems associated with linear skew symmetric operator. Proceedings 16th International symposium on Mathematical Theory of Networks and Systems: Leuven, Belgium, July 5-9, 2004. editor / Bart De Mor ; Bart Motmans ; Jan Willems ; Paul Van Dooren ; Vincent Blondel. Leuven, Belgium : Katholieke Universiteit Leuven, 2004.

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title = "A semigroup approach to Port Hamiltonian systems associated with linear skew symmetric operator",

abstract = "In this paper we first define a Dirac structure on a Hilbert spaces associated with a skew-symmetric linear operator including port variables on the boundary of its domain. Secondly, we associate \$C\_0\$-semigroup with some parameterization of the boundary port variables and define a family of boundary control systems. Thirdly we define a linear port controlled Hamiltonian system associated with the previously defined Dirac structure and generated by a symmetric positive operator defining the energy of the system.",

keywords = "MSC-93C20",

author = "\{Le Gorrec\}, Y. and H. Zwart and B. Maschke",

year = "2004",

language = "English",

isbn = "90-5682-517-8",

editor = "\{De Mor\}, Bart and Bart Motmans and Jan Willems and \{Van Dooren\}, Paul and Vincent Blondel",

booktitle = "Proceedings 16th International symposium on Mathematical Theory of Networks and Systems",

publisher = "Katholieke Universiteit Leuven",

note = "16th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2004, MTNS ; Conference date: 05-07-2004 Through 09-07-2004",

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Le Gorrec, Y, Zwart, H & Maschke, B 2004, A semigroup approach to Port Hamiltonian systems associated with linear skew symmetric operator. in B De Mor, B Motmans, J Willems, P Van Dooren & V Blondel (eds), Proceedings 16th International symposium on Mathematical Theory of Networks and Systems: Leuven, Belgium, July 5-9, 2004. Katholieke Universiteit Leuven, Leuven, Belgium, 16th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2004, Leuven, Belgium, 5/07/04.

A semigroup approach to Port Hamiltonian systems associated with linear skew symmetric operator. / Le Gorrec, Y.; Zwart, H.; Maschke, B.
Proceedings 16th International symposium on Mathematical Theory of Networks and Systems: Leuven, Belgium, July 5-9, 2004. ed. / Bart De Mor; Bart Motmans; Jan Willems; Paul Van Dooren; Vincent Blondel. Leuven, Belgium: Katholieke Universiteit Leuven, 2004.

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

TY - GEN

T1 - A semigroup approach to Port Hamiltonian systems associated with linear skew symmetric operator

AU - Le Gorrec, Y.

AU - Zwart, H.

AU - Maschke, B.

N1 - Conference code: 16

PY - 2004

Y1 - 2004

N2 - In this paper we first define a Dirac structure on a Hilbert spaces associated with a skew-symmetric linear operator including port variables on the boundary of its domain. Secondly, we associate $C_0$-semigroup with some parameterization of the boundary port variables and define a family of boundary control systems. Thirdly we define a linear port controlled Hamiltonian system associated with the previously defined Dirac structure and generated by a symmetric positive operator defining the energy of the system.

AB - In this paper we first define a Dirac structure on a Hilbert spaces associated with a skew-symmetric linear operator including port variables on the boundary of its domain. Secondly, we associate $C_0$-semigroup with some parameterization of the boundary port variables and define a family of boundary control systems. Thirdly we define a linear port controlled Hamiltonian system associated with the previously defined Dirac structure and generated by a symmetric positive operator defining the energy of the system.

KW - MSC-93C20

M3 - Conference contribution

SN - 90-5682-517-8

BT - Proceedings 16th International symposium on Mathematical Theory of Networks and Systems

A2 - De Mor, Bart

A2 - Motmans, Bart

A2 - Willems, Jan

A2 - Van Dooren, Paul

A2 - Blondel, Vincent

PB - Katholieke Universiteit Leuven

CY - Leuven, Belgium

T2 - 16th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2004

Y2 - 5 July 2004 through 9 July 2004

ER -

Le Gorrec Y, Zwart H, Maschke B. A semigroup approach to Port Hamiltonian systems associated with linear skew symmetric operator. In De Mor B, Motmans B, Willems J, Van Dooren P, Blondel V, editors, Proceedings 16th International symposium on Mathematical Theory of Networks and Systems: Leuven, Belgium, July 5-9, 2004. Leuven, Belgium: Katholieke Universiteit Leuven. 2004

A semigroup approach to Port Hamiltonian systems associated with linear skew symmetric operator

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