Stability analysis of discontinuous quantum control systems with dipole and polarizability coupling

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 recently been proposed to control these types of system. 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 the LaSalle invariance principle for differential inclusions. Numerical simulations are included to illustrate the efficiency of the discontinuous control.