Journal
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
Volume 44, Issue 5, Pages 1864-1892Publisher
SIAM PUBLICATIONS
DOI: 10.1137/040611677
Keywords
port Hamiltonian systems; strongly continuous semigroup; boundary control systems; Dirac structures
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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 in finite- 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 de. ne a linear port controlled Hamiltonian system associated with the previously defined Dirac structure and a symmetric positive operator de. ning the energy of the system. We illustrate this theory on the example of the Timoshenko beam.
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