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.
|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|
|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||16th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2004|
|Period||5/07/04 → 9/07/04|
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 Leuven, Belgium: Katholieke Universiteit Leuven.