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arXiv · 2509.02212

Finite-Time Stabilization of a Class of Nonlinear Systems in Hilbert Space

Kamal Fenza·Moussa Labbadi·Mohamed Ouzahra
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Abstract

This paper deals with the finite-time stabilization of a class of nonlinear infinite-dimensional systems. First, we consider a bounded matched perturbation in its linear form. It is shown that by using a set-valued function, both the convergence objective (finite-time) and the rejection of perturbations are achieved. Second, we consider a class of nonlinear systems and design a feedback control that ensures the closed-loop system is finite-time stable. All proofs presented in this paper regarding convergence are based on Lyapunov theory. The existence of solutions to the closed-loop system and its well-posedness are established using maximal monotone theory. To illustrate the applicability of the theoretical results, a heat equation is considered as an application of the main results.

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Kamal Fenza, Moussa Labbadi, Mohamed Ouzahra. 2025-09-02. Finite-Time Stabilization of a Class of Nonlinear Systems in Hilbert Space. https://arxiv.org/abs/2509.02212

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