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

摘要

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.