| Title: |
Feedback stabilization of some fourth-order nonlinear parabolic equations with saturared controls |
| Authors: |
Guzmán, Patricio; Labra, Felipe; Parada, Hugo |
| Contributors: |
Universidad Tecnica Federico Santa Maria Valparaiso (UTFSM); Facultad de Matemáticas Santiago de Chile; Pontificia Universidad Católica de Chile = Pontifical Catholic University of Chile Santiago (PUC); Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (SPHINX); Centre Inria de l'Université de Lorraine; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Élie Cartan de Lorraine (IECL); Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS); Institut Élie Cartan de Lorraine (IECL); Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS); P. Guzmán received partial financial support from FONDECYT 11240290.; ANR-24-CE40-3008,QuBiCCS,Contrôle Bilinéaire Quantique avec spectre continu(2024) |
| Source: |
https://hal.science/hal-05398937 ; 2026. |
| Publisher Information: |
CCSD |
| Publication Year: |
2026 |
| Collection: |
Université de Lorraine: HAL |
| Subject Terms: |
Stabilization; Saturation; PDE control; Modal decomposition; Lyapunov functional; [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]; [INFO.INFO-SY]Computer Science [cs]/Systems and Control [cs.SY]; [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] |
| Description: |
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. |
| Document Type: |
report |
| Language: |
English |
| Availability: |
https://hal.science/hal-05398937; https://hal.science/hal-05398937v3/document; https://hal.science/hal-05398937v3/file/sat_KSNuevo.pdf |
| Rights: |
https://creativecommons.org/licenses/by/4.0/ ; info:eu-repo/semantics/OpenAccess |
| Accession Number: |
edsbas.3AA8B2E3 |
| Database: |
BASE |