### Abstract

Original language | Undefined |
---|---|

Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Publication status | Published - 2004 |

### Publication series

Name | Memorandum / Faculty of Mathematical Sciences |
---|---|

Publisher | Department of Applied Mathematics, University of Twente |

No. | 1730 |

ISSN (Print) | 0169-2690 |

### Keywords

- MSC-93C25
- MSC-35M99
- MSC-70H45
- IR-65914
- EWI-3550
- MSC-47D06
- MSC-93C20

### Cite this

*Dirac structures and boundary control systems associated with skew-symmetric differential operators*. (Memorandum / Faculty of Mathematical Sciences; No. 1730). Enschede: University of Twente, Department of Applied Mathematics.

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*Dirac structures and boundary control systems associated with skew-symmetric differential operators*. Memorandum / Faculty of Mathematical Sciences, no. 1730, University of Twente, Department of Applied Mathematics, Enschede.

**Dirac structures and boundary control systems associated with skew-symmetric differential operators.** / Le Gorrec, Y.; Zwart, Heiko J.; Maschke, B.M.

Research output: Book/Report › Report › Other research output

TY - BOOK

T1 - Dirac structures and boundary control systems associated with skew-symmetric differential operators

AU - Le Gorrec, Y.

AU - Zwart, Heiko J.

AU - Maschke, B.M.

N1 - Imported from MEMORANDA

PY - 2004

Y1 - 2004

N2 - Associated with a skew-symmetric linear operator on the spatial domain $[a,b]$ we define a Dirac structure which includes the port variables on the boundary of this spatial domain. This Dirac structure is a subspace of a Hilbert space. Naturally, associated to this Dirac structure is infinite dimensional system. We parameterize the boundary port variables for which the \( C_{0} \)-semigroup associated to this system is contractive or unitary. Furthermore, this parameterization is used to split the boundary port variables into inputs and outputs. Similarly, we define a linear port controlled Hamiltonian system associated with the previously defined Dirac structure and a symmetric positive operator defining the energy of the system. We illustrate this theory on the example of the Timoshenko Beam.

AB - Associated with a skew-symmetric linear operator on the spatial domain $[a,b]$ we define a Dirac structure which includes the port variables on the boundary of this spatial domain. This Dirac structure is a subspace of a Hilbert space. Naturally, associated to this Dirac structure is infinite dimensional system. We parameterize the boundary port variables for which the \( C_{0} \)-semigroup associated to this system is contractive or unitary. Furthermore, this parameterization is used to split the boundary port variables into inputs and outputs. Similarly, we define a linear port controlled Hamiltonian system associated with the previously defined Dirac structure and a symmetric positive operator defining the energy of the system. We illustrate this theory on the example of the Timoshenko Beam.

KW - MSC-93C25

KW - MSC-35M99

KW - MSC-70H45

KW - IR-65914

KW - EWI-3550

KW - MSC-47D06

KW - MSC-93C20

M3 - Report

T3 - Memorandum / Faculty of Mathematical Sciences

BT - Dirac structures and boundary control systems associated with skew-symmetric differential operators

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -