A Decomposition Method for Finite-Time Stabilization of Bilinear Systems with Applications to Parabolic and Hyperbolic Equations
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909660011823104 |
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| author | Fenza, Kamal Labbadi, Moussa Ouzahra, Mohamed |
| author_facet | Fenza, Kamal Labbadi, Moussa Ouzahra, Mohamed |
| contents | In this work, we address the problem of finite-time stabilization for a class of bilinear system. We propose a decomposition-based approach in which the nominal system is split into two subsystems, one of which is inherently finite-time stable without control. This allows the stabilization analysis to focus solely on the remaining subsystem. To ensure the well-posedness of the closed-loop system, we establish sufficient conditions on the system and control operators. The stabilization results are then derived using a suitable Lyapunov function and an observation condition. The effectiveness of the proposed approach is demonstrated through examples involving both parabolic and hyperbolic infinite-dimensional systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_20492 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Decomposition Method for Finite-Time Stabilization of Bilinear Systems with Applications to Parabolic and Hyperbolic Equations Fenza, Kamal Labbadi, Moussa Ouzahra, Mohamed Optimization and Control Systems and Control In this work, we address the problem of finite-time stabilization for a class of bilinear system. We propose a decomposition-based approach in which the nominal system is split into two subsystems, one of which is inherently finite-time stable without control. This allows the stabilization analysis to focus solely on the remaining subsystem. To ensure the well-posedness of the closed-loop system, we establish sufficient conditions on the system and control operators. The stabilization results are then derived using a suitable Lyapunov function and an observation condition. The effectiveness of the proposed approach is demonstrated through examples involving both parabolic and hyperbolic infinite-dimensional systems. |
| title | A Decomposition Method for Finite-Time Stabilization of Bilinear Systems with Applications to Parabolic and Hyperbolic Equations |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2506.20492 |