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infinite–dimensional system

Mathematical Modelling of Natural Phenomena (1)

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A Kernel Representation of Dirac Structures forInfinite-dimensional Systems
O.V. Iftime, M. Roman, A. Sandovici
Journal:

Mathematical Modelling of Natural Phenomena / Volume 9 / Issue 5 / 2014

Published online by Cambridge University Press:

19 August 2014, pp. 295-308

Print publication:

2014
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Dirac structures are used as the underlying structure to mathematically formalizeport-Hamiltonian systems. This note approaches the Dirac structures forinfinite-dimensional systems using the theory of linear relations on Hilbert spaces.First, a kernel representation for a Dirac structure is proposed. The one-to-onecorrespondence between Dirac structures and unitary operators is revisited. Further, theproposed kernel representation and a scattering representation are constructively related.Several illustrative examples are also presented in the paper.