A note on positively invariant cones

Given a closed convex pointed cone which is positively invariant with respect to motions of the differential equation (A being a real (n × n) matrix), it is proven that a necessary and sufficient condition for asymptotic stability of (and therefore of the linear span of) is In case, this result yields a known equivalence from the theory ofM-matrices.This research was supported by the Natural Sciences and Engineering Council Canada under grant A4641.