### 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 |
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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 |
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Abbreviated title | MTNS |

Country | Belgium |

City | Leuven |

Period | 5/07/04 → 9/07/04 |

### Keywords

- MSC-93C20

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## Cite this

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.