Hautus-Yamamoto criteria for approximate and exact controllability of difference delay equations

Sébastien Fueyo

Jeudi 20 octobre, 14h, salle Coriolis (Galois).

Abstract. The talk deals with the controllability of difference delay equations. Based on the realization theory developed by Y. Yamamoto for general infinite dimensional dynamical systems, we obtain necessary and/or sufficient conditions, expressed in the frequency domain, for the approximate and/or exact controllability in finite time of difference delay equations. Furthermore, we provide an explicit upper bound on the minimal time of controllability. The main ingredient to tackle the problem is the solvability of a Bézout identity over a Radon measure algebra (and its associated Corona problem).