  One version of the concept of structural controllability defined for
single-input systems by Lin and subsequently generalized to multi-input systems
by others, states that a parameterized matrix pair $(A, B)$ whose nonzero
entries are distinct parameters, is structurally controllable if values can be
assigned to the parameters which cause the resulting matrix pair to be
controllable. In this paper the concept of structural controllability is
broadened to allow for the possibility that a parameter may appear in more than
one location in the pair $(A, B)$. Subject to a certain condition on the
parameterization called the "binary assumption", an explicit graph-theoretic
characterization of such matrix pairs is derived.
