Year: 2026
Type: article
Abstract: We adapt an optimization technique, originally developed for quadratic matrix model updating problems, to construct optimal stabilizers for linearized partial differential equations (PDEs). The proposed approach is flexible, allowing the optimization of mass, damping, and stiffness operators either individually or simultaneously. It is also straightforward to implement within standard numerical frameworks. We analyze the numerical and practical properties of the method, highlighting its robustness even with low-order discretizations and its capacity to produce interpretable stabilization operators. The effectiveness and versatility of the approach are demonstrated through numerical experiments on several representative linearized PDEs, including the Klein–Gordon, Boussinesq, Benjamin–Bona–Mahony, and Korteweg–de Vries equations. Our results indicate that the method provides a unified, efficient, and modular tool for PDE stabilization.
Institutions: Centre National de la Recherche Scientifique, Laboratoire Amiénois de Mathématique Fondamentale et Appliquée, Université de Picardie Jules Verne, Lyon 1 Université, École Centrale de Lyon, Institut Camille Jordan, Université Jean Monnet, Institut National des Sciences Appliquées de Lyon, Université Jean Monnet, Universidade Nova de Lisboa
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W7213559534