Contrôlabilité exacte pour l'équation des ondes avec contraintes sur le contrôle
We consider the exact controllability and stabilization of Maxwell equation by using results on the propagation of singularities of the electromagnetic field. We will assume geometrical control condition and use techniques of the work of Bardos et al. on the wave equation. The problem of internal stabilization will be treated with more attention because the condition divE=0 is not preserved by the system of Maxwell with Ohm's law.
Interpretations of most existing controllability and observability notions for linear delay systems are given. Module theoretic characterizations are presented. This setting enables a clear and precise comparison of the various examined notions. A new notion of controllability is introduced, which is called pi-freeness.