On exact Observability for Compactly perturbed infinite dimension system
Analysis of PDEs
2026-01-01 v1
Abstract
In this paper, we study the observability of compactly perturbed infinite dimensional systems. Assuming that a given infinite-dimensional system with self-adjoint generator is exactly observable we derive sufficient conditions on a compact self adjoint perturbation to guarantee that the perturbed system stays exactly observable. The analysis is based on a careful asymptotic estimation of the spectral elements of the perturbed unbounded operator in terms of the compact perturbation. These intermediate results are of importance themselves.
Cite
@article{arxiv.2512.25041,
title = {On exact Observability for Compactly perturbed infinite dimension system},
author = {Nisrine Charaf and Faouzi Triki},
journal= {arXiv preprint arXiv:2512.25041},
year = {2026}
}