On Robust Fixed-Time Stabilization of the Cauchy Problem in Hilbert Spaces
Systems and Control
2026-02-12 v2 Systems and Control
Abstract
This paper presents finite-time and fixed-time stabilization results for inhomogeneous abstract evolution problems, extending existing theories. We prove well-posedness for strong and weak solutions, and estimate upper bounds for settling times for both homogeneous and inhomogeneous systems. We generalize finite-dimensional results to infinite-dimensional systems and demonstrate partial state stabilization with actuation on a subset of the domain. The interest of these results are illustrated through an application of a heat equation with memory term.
Cite
@article{arxiv.2601.08335,
title = {On Robust Fixed-Time Stabilization of the Cauchy Problem in Hilbert Spaces},
author = {Moussa Labbadi and Christophe Roman and Yacine Chitour},
journal= {arXiv preprint arXiv:2601.08335},
year = {2026}
}
Comments
The paper has some problems in the proofs