  In this paper, we study the simultaneous controllability of wave systems in
an open domain of R d , d $\in$ N *. We obtain a partial controllability result
on a co-finite dimensional space for wave equations coupled by a single control
function. We use microlocal defect measures and the unique continuation
property of eigenfunctions to prove that an appropriate observability
inequality holds for wave equations with space varying and different speeds
coupled by a single control function. For the unique continuation property of
eigenfunctions, we construct a counterexample to show that in some metrics, the
unique continuation property does not hold. Moreover, we study different
conditions to ensure the unique continuation property. We also extend our
result to the case of constant coefficients and possibly multiple control
functions. In this context, we prove the controllability property is equivalent
to an appropriate Kalman rank condition.
