Controlability, observability, and duality in a distributed parameter system with continuous and point spectrum

The controllability of a specific system which is representative of the class of self-adjoint parabolic distributed parameter systems defined on a semi-infinite interval is established. Such systems possess nonempty continuous and/or point spectrum. Necessary and sufficient conditions for observability of the system are derived and, in the case where the observation is made at the boundary, a dual system is developed.