  In this paper, we study the exact controllability and stabilization of a
system of two wave equations coupled by velocities with an internal, local
control acting on only one equation. We distinguish two cases. In the first
one, when the waves propagate at the same speed: using a frequency domain
approach combined with multiplier technique, we prove that the system is
exponentially stable when the coupling region satisfies the geometric control
condition GCC. Following a result of Haraux ([11]), we establish the main
indirect observability inequality. This results leads, by the HUM method, to
prove that the total system is exactly controllable by means of locally
distributed control. In the second case, when the waves propagate at different
speed, we establish an exponential decay rate in the weak energy space.
Consequently, the system is exactly controllable using a result of [11].
