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

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Le Gorrec, Y. and Zwart, H.J. and Maschke, B. (2005) Dirac structures and boundary control systems associated with skew-symmetric differential operators. SIAM Journal on Control and Optimization, 44 (5). pp. 1864-1892. ISSN 0363-0129

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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 with this Dirac structure is an infinite-dimensional system. We parameterize the boundary port variables for which the $C_{0}$-semigroup associated with 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.
Item Type:Article
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Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/65639
Official URL:http://dx.doi.org/10.1137/040611677
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