We consider Maxwell's equations with the Silver-Miller absorbing bound
ary conditions in a bounded domain of R3. Assuming that the domain is
star-shaped we prove the exponential energy decay of the solutions. As
a consequence, we improve some earlier exact controllability theorems
by weakening their time assumptions. Our results are optimal if OMEGA
is a ball. The proofs are based on a new identity obtained by the mul
tiplier method.