  This paper deals with strong structural controllability of linear structured
systems in which the system matrices are given by zero/nonzero/arbitrary
pattern matrices. Instead of assuming that the nonzero and arbitrary entries of
the system matrices can take their values completely independently, this paper
allows equality constraints on these entries, in the sense that {\em a priori}
given entries in the system matrices are restricted to take arbitrary but
identical values. To formalize this general class of structured systems, we
introduce the concepts of colored pattern matrices and colored structured
systems. The main contribution of this paper is that it generalizes both the
classical results on strong structural controllability of structured systems as
well as recent results on controllability of systems defined on colored graphs.
In this paper, we will establish both algebraic and graph-theoretic conditions
for strong structural controllability of this more general class of structured
systems.
