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

Grigoriu, Andreea

Grigoriu, Andreea (2012), Stability analysis of discontinous quantum control systems with dipole and polarizability coupling, Automatica, 48, 9, p. 2229–2234. http://dx.doi.org/10.1016/j.automatica.2012.06.028

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00578341/en/

Date

2012

Journal name

Automatica

Volume

Number

Publisher

Elsevier

Pages

2229–2234

Abstract (EN)

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.

Subjects / Keywords

Diﬀerential inclusions; Tracking; Control Lyapunov function; Stabilization; Quantum systems