  An alternative formulation for the controllability problem of single input
linear positive systems is presented. Driven by many industrial applications,
this formulations focuses on the case where the region of interest is only a
subset of positive orthant rather than the entire positive orthant. To this
end, we discuss the geometry of controllable subsets and develop numerically
verifiable conditions for polyhedrality of controllable subsets. Finally, we
provide a method to check for controllability of a target set based on our
approach.
