A point of a convex set belongs to its end in a given direction when this d
irection is not feasible at that point. This paper analyzes the properties
of the directional end of general convex sets and closed convex sets (for w
hich the directional ends are connected by arcs) as well as the relationshi
p between the directional end and certain concepts on the illumination of c
onvex bodies. The paper includes applications of the directional end to the
theory of linear systems.