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

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
48
Number
9
Publisher
Elsevier
Pages
2229–2234
Publication identifier
http://dx.doi.org/10.1016/j.automatica.2012.06.028
Metadata
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Author(s)
Grigoriu, Andreea
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

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