  We consider the notion of herdability, a set-based reachability condition,
which asks whether the state of a system can be controlled to be element-wise
larger than a non-negative threshold. First a number of foundational results on
herdability of a continuous time, linear time invariant system are presented.
These show that the herdability of a linear system can be determined based on
certain matrices, such as the controllability matrix, which arise in the study
of controllability of linear systems. Second, the relationship between the sign
pattern of the underlying graph structure of a system and the herdability
properties of the system is investigated. In doing so the notion of sign
herdability is introduced which captures classes of systems whose sign pattern
determines their herdability. We identify a set of conditions, first on the
sign pattern of the controllability matrix and then on the underlying graph
structure, that ensure that the system is sign herdable.
