The Hautus test for infinite dimensional systems
Marius TUCSNAK
Institut Elie Cartan de Nancy
Plan of the talk
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Background on exact observability
•
The Hautus test
•
High and low frequency decomposition
•
From the wave to the Schrödinger equation
•
A problem of fluid structure interaction
2
Background on exact observability
4
The duality observability-controllability
5
The wave equation with
Neumann boundary observation
6
The Hautus test
The finite dimensional case
8
9
The Russell-Weiss necessary condition
10
Sketch of the proof (I)
11
Sketch of the proof (II)
12
The skew-adjoint case
13
Proof of the necessity
14
High and low frequency decomposition
First decomposition result
16
Application to the Hautus test (I)
17
Application to the Hautus test (II)
18
From the wave to the Schrödinger equation
Notation
20
21
The Schrödinger equation with
Neumann boundary observation
22
A problem of fluid structure interaction
Statement of the problem
24
The controllability result (I)
25
The controllability result (II)
26
27