English

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.

Keywords

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

R2 v1 2026-07-01T09:02:24.458Z