We study the rapid stabilization of general linear systems, when the differential operator $\mathcal{A}$ has a Riesz basis of eigenvectors. We find simple sufficient conditions for the rapid stabilization and the construction of a relatively explicit feedback operator. We use an $F$-equivalence approach \textcolor{black}{relying on Fredholm transformation} to show a stronger result: under these sufficient conditions the system is equivalent to a simple exponentially stable system, with arbitrarily large decay rate. In particular, our conditions improve the existing conditions of rapid stabilization for non-parabolic operators such as skew-adjoint systems.
Theorical and Numerical Analysis of the Rapid Pointwise Stabilization of Coupled String-Beam Systems
Institut Supérieur d’Informatique et de Mathématiques de Monastir（莫纳斯特尔信息与数学高等学院）；Université de Monastir（莫纳斯特尔大学）；Institut de Rechrche Mathématique Avancée, Université de Strasbourg（斯特拉斯堡大学高级数学研究所）
Quantitative Fredholm backstepping and rapid stabilization
Peking University（北京大学）；Sorbonne Université, CNRS, Inria équipe CAGE（索邦大学，法国国家科学研究中心，Inria CAGE团队）；Université de Lorraine, CNRS, Inria（洛林大学，法国国家科学研究中心，Inria）；CERMICS, École des Ponts ParisTech（巴黎路桥学院 CERMICS）；LS2N, Ecole Centrale de Nantes & CNRS UMR 6004（南特中央理工学院 LS2N 与法国国家科学研究中心 UMR 6004）
