Controllability of a multichannel system

We consider the system consisting of K coupled acoustic channels with the different sound velocities $c_j$. Channels are interacting at any point via the pressure and its time derivatives. Using the moment approach and the theory of exponential families with vector coefficients we establish two controllability results: the system is exactly controllable if(i) the control $u_j$ in the jth channel acts longer than the double travel time of a wave from the start to the end of the j-th channel;(ii) all controls $u_j$ act more than or equal to the maximal double travel time.