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arXiv · 1005.4558

Semi-global weak stabilization of bilinear Schr\"odinger equations

Karine Beauchard·Vahagn Nersesyan
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Abstract

We consider a linear Schr\"odinger equation, on a bounded domain, with bilinear control, representing a quantum particle in an electric field (the control). Recently, Nersesyan proposed explicit feedback laws and proved the existence of a sequence of times $(t_n)_{n \in \mathbb{N}}$ for which the values of the solution of the closed loop system converge weakly in $H^2$ to the ground state. Here, we prove the convergence of the whole solution, as $t \rightarrow + \infty$. The proof relies on control Lyapunov functions and an adaptation of the LaSalle invariance principle to PDEs.

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Karine Beauchard, Vahagn Nersesyan. 2010-05-25. Semi-global weak stabilization of bilinear Schr\"odinger equations. https://arxiv.org/abs/1005.4558

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