If lashed to a saddle bag the long slender weight of the mat will
likely put too much torque on the leather straps and the whole thing
will sway too much, at least in my experience.
For short trips you can lay or strap it on the top of the drops behind
the hoods as well. If using a mat it is my thick heavy Munduka, and
requires a pretty solid lashing as well as the fact that it is kind of
bulky for sling cary. Lashed to my bagman as previously posted works
well, but it can also be lashed longways to any rack. Paniers work
well too, just leave it sticking out of the top.
Where ther is a will there will be a way.
Rob