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arXiv · 1802.09224

Controllability and observability for non-autonomous evolution equations: the averaged Hautus test

Bernhard Haak·Duc-Trung Hoang·El-Maati Ouhabaz
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Abstract

We consider the observability problem for non-autonomous evolution systems (i.e., the operators governing the system depend on time). We introduce an averaged Hautus condition and prove that for skew-adjoint operators it characterizes exact observability. Next, we extend this to more general class of operators under a growth condition on the associated evolution family. We give an application to the Schr\"odinger equation with time dependent potential and the damped wave equation with a time dependent damping coefficient.

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Bernhard Haak, Duc-Trung Hoang, El-Maati Ouhabaz. 2018-02-26. Controllability and observability for non-autonomous evolution equations: the averaged Hautus test. https://arxiv.org/abs/1802.09224

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