Stabilization and controllability of first-order integro-differential hyperbolic equations
Optimization and Control
2015-11-04 v1
Abstract
In the present article we study the stabilization of first-order linear integro-differential hyperbolic equations. For such equations we prove that the stabilization in finite time is equivalent to the exact controllability property. The proof relies on a Fredholm transformation that maps the original system into a finite-time stable target system. The controllability assumption is used to prove the invertibility of such a transformation. Finally, using the method of moments, we show in a particular case that the controllability is reduced to the criterion of Fattorini.
Cite
@article{arxiv.1511.01078,
title = {Stabilization and controllability of first-order integro-differential hyperbolic equations},
author = {Jean-Michel Coron and Long Hu and Guillaume Olive},
journal= {arXiv preprint arXiv:1511.01078},
year = {2015}
}