  In this article, a new notion of modal strong structural controllability is
introduced and examined for a family of LTI networks. These networks include
structured LTI subsystems, whose system matrices have the same
zero/nonzero/arbitrary pattern. An eigenvalue associated with a system matrix
is controllable if it can be directly influenced by the control inputs. We
consider an arbitrary set \Delta, and we refer to a network as modal strongly
structurally controllable with respect to \Delta if, for all systems in a
specific family of LTI networks, every \lambda\in\Delta is a controllable
eigenvalue. For this family of LTI networks, not only is the
zero/nonzero/arbitrary pattern of system matrices available, but also for a
given \Delta, there might be extra information about the intersection of the
spectrum associated with some subsystems and \Delta. Given a set \Delta, we
first define a \Delta-network graph, and by introducing a coloring process of
this graph, we establish a correspondence between the set of control subsystems
and the so-called zero forcing sets. We also demonstrate how with \Delta={0} or
\Delta=C\{0}, existing results on strong structural controllability can be
derived through our approach. Compared to relevant literature, a more
restricted family of LTI networks is considered in this work, and then, the
derived condition is less conservative.
