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A Kernel Representation of Dirac Structures for Infinite-dimensional Systems

Published online by Cambridge University Press:  19 August 2014

O.V. Iftime ,
M. Roman  and
A. Sandovici
O.V. Iftime
Affiliation:
Department of Economics, Econometrics and Finance, University of Groningen Nettelbosje 2, 9747 AE, Groningen, The Netherlands
M. Roman
Affiliation:
Department of Mathematics, “Gheorghe Asachi” Technical University B-dul Carol I, nr. 11, 700506, Iaşi, Romania
A. Sandovici*
Affiliation:
Department of Mathematics, “Gheorghe Asachi” Technical University B-dul Carol I, nr. 11, 700506, Iaşi, Romania
*
⋆ Corresponding author. E-mail: adrian.sandovici@luminis.ro
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Abstract

Dirac structures are used as the underlying structure to mathematically formalize port-Hamiltonian systems. This note approaches the Dirac structures for infinite-dimensional systems using the theory of linear relations on Hilbert spaces. First, a kernel representation for a Dirac structure is proposed. The one-to-one correspondence between Dirac structures and unitary operators is revisited. Further, the proposed kernel representation and a scattering representation are constructively related. Several illustrative examples are also presented in the paper.

Keywords

Dirac structurelinear relationHilbert spaceinfinite–dimensional system
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 9 , Issue 5: Spectral problems , 2014 , pp. 295 - 308
Copyright
© EDP Sciences, 2014

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