  Suppose that A and B are real stable matrices, and that their difference A-B
is rank one. Then A and B have a common quadratic Lyapunov function if and only
if the product AB has no real negative eigenvalue. This result is due to
Shorten and Narendra, who showed that it follows as a consequence of the
Kalman-Yacubovich-Popov solution of the Lur'e problem. Here we present a new
and independent proof based on results from convex analysis and the theory of
moments.
