Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rapid Stabilization of a Linearized Bilinear $1-D$ Schr\"odinger
  Equation   We consider the one dimensional Schr\"odinger equation with a bilinear
control and prove the rapid stabilization of the linearized equation around the
ground state. The feedback law ensuring the rapid stabilization is obtained
using a transformation mapping the solution to the linearized equation on the
solution to an exponentially stable target linear equation. A suitable
condition is imposed on the transformation in order to cancel the non-local
terms arising in the kernel system. This conditions also insures the uniqueness
of the transformation. The continuity and invertibility of the transformation
follows from exact controllability of the linearized system.

29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph