Controllability and observability for non-autonomous evolution equations: the averaged Hautus test
Analysis of PDEs
2018-02-27 v1 Optimization and Control
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.
Cite
@article{arxiv.1802.09224,
title = {Controllability and observability for non-autonomous evolution equations: the averaged Hautus test},
author = {Bernhard Haak and Duc-Trung Hoang and El-Maati Ouhabaz},
journal= {arXiv preprint arXiv:1802.09224},
year = {2018}
}
Comments
14p