A Kernel Representation of Dirac Structures for Infinite-dimensional Systems. (19th August 2014)

• Record Type: Journal Article
• Authors: Iftime, O.V.; Roman, M.; Sandovici, A.
• Editors: Damanik, David; Ruzhansky, Michael; Vougalter, Vitali; Wong, M.W.
• Is Part Of: Mathematical modelling of natural phenomena. Volume 9:Number 5(2014)
• Page Start: 295
• Page End: 308
• Publication Date: 2014-08-19
• Subjects: Dirac structure, -- linear relation, -- Hilbert space, -- infinite–dimensional system; Science -- Mathematical models -- Periodicals; Medicine -- Mathematical models -- Periodicals; Biology -- Mathematical models -- Periodicals; 501.51
• DOI: 10.1051/mmnp/20149520
• Languages: English
• ISSNs: 0973-5348

Abstract

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.