Simultaneous Control of Wave Systems

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