@book{74e466ea9eae436ba30dae5dd322f412,
title = "Dirac structures and boundary control systems associated with skew-symmetric differential operators",
abstract = "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.",
keywords = "MSC-93C25, MSC-35M99, MSC-70H45, MSC-47D06, MSC-93C20",
author = "{Le Gorrec}, Y. and H.J. Zwart and B. Maschke",
year = "2004",
language = "English",
series = "Memorandum / Faculty of Mathematical Sciences",
publisher = "University of Twente",
number = "1730",
address = "Netherlands",
}