Feedback stabilization of some fourth-order nonlinear parabolic equations with saturated controls
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915683375251456 |
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| author | Guzmán, Patricio Labra, Felipe Parada, Hugo |
| author_facet | Guzmán, Patricio Labra, Felipe Parada, Hugo |
| contents | In this work, we analyze the internal and boundary stabilization of the Cahn-Hilliard and Kuramoto-Sivashinsky equations under saturated feedback control. We conduct our study through the spectral analysis of the associated linear operator. We identify a finite number of eigenvalues related to the unstable part of the system and then design a stabilization strategy based on modal decomposition, linear matrix inequalities (LMIs), and geometric conditions on the saturation function. Local exponential stabilization in $H^{2}$ is established. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_05606 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Feedback stabilization of some fourth-order nonlinear parabolic equations with saturated controls Guzmán, Patricio Labra, Felipe Parada, Hugo Systems and Control Analysis of PDEs Optimization and Control In this work, we analyze the internal and boundary stabilization of the Cahn-Hilliard and Kuramoto-Sivashinsky equations under saturated feedback control. We conduct our study through the spectral analysis of the associated linear operator. We identify a finite number of eigenvalues related to the unstable part of the system and then design a stabilization strategy based on modal decomposition, linear matrix inequalities (LMIs), and geometric conditions on the saturation function. Local exponential stabilization in $H^{2}$ is established. |
| title | Feedback stabilization of some fourth-order nonlinear parabolic equations with saturated controls |
| topic | Systems and Control Analysis of PDEs Optimization and Control |
| url | https://arxiv.org/abs/2512.05606 |