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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.02212 |
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| _version_ | 1866912566615212032 |
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| author | Fenza, Kamal Labbadi, Moussa Ouzahra, Mohamed |
| author_facet | Fenza, Kamal Labbadi, Moussa Ouzahra, Mohamed |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02212 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite-Time Stabilization of a Class of Nonlinear Systems in Hilbert Space Fenza, Kamal Labbadi, Moussa Ouzahra, Mohamed Systems and Control 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. |
| title | Finite-Time Stabilization of a Class of Nonlinear Systems in Hilbert Space |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2509.02212 |