Continuously equivalent state variable realizations

Suppose one is given two minimal realizations of the same transfer function matrix. The question is asked: When does there exist a family of coordinate transformations defined by a set of nonsingular matrices
T(\lambda)
, continuously dependent on
\lambda
, with
T(0) = I
and with
(1)
mapping the state vector associated with one minimal realization into the state vector associated with the other? The quesion is answered, and a procedure is given for constructing the family when it exists.