  This paper provides a general theory for characterizing and constructing a
decoherence-free (DF) subsystem for an infinite dimensional linear open quantum
system. The main idea is that, based on the Heisenberg picture of the dynamics
rather than the commonly-taken Schrodinger picture, the notions of
controllability and observability in control theory are employed to
characterize a DF subsystem. A particularly useful result is a general if and
only if condition for a linear system to have a DF component; this condition is
used to demonstrate how to actually construct a DF dynamics in some specific
examples. It is also shown that, as in the finite dimensional case, we are able
to do coherent manipulation and preservation of a state of a DF subsystem.
