Résumé en anglais

Closed quantum systems under the influence of a laser field, whose interaction is modeled by a Schrödinger equation with a coupling control operator containing both a linear (dipole) and a quadratic (polarizability) term are analyzed. Discontinuous feedbacks, obtained by a Lyapunov trajectory tracking procedure, have been recently proposed to control these type of systems. The purpose of this paper is to study the asymptotic stability by considering the solutions in the Filippov sense. The analysis is developed by applying a variant of LaSalle invariance principle for differential inclusions. Numerical simulations are included to illustrate the efficiency of the discontinuous control.