Une nouvelle approche pour la synchronisation approchée d'un système couplé d'équations des ondes : contrôles directs et indirects

In this Note, we give a new and more natural definition of the approximate synchronization by p-groups (p≥1) for a coupled system of N wave equations with Dirichlet boundary controls. By means of Kalman's criterion, the concept of the number of total (direct and indirect) controls is introduced. If the minimal number of total controls is equal to (N−p), then the existence of the approximately synchronizable state as well as the necessity of the Cp-compatibility condition are the consequence of the approximate synchronization by p-groups. Otherwise, the approximate synchronization by p-groups could imply some unexpected additional properties.