Auriol, JeanMorris, KirstenDi Meglio, Florent2020-07-062020-07-062019-02https://doi.org/10.1016/j.automatica.2018.11.024http://hdl.handle.net/10012/16039The final publication is available at Elsevier via https://doi.org/10.1016/j.automatica.2018.11.024. © 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/We consider in this paper three different partial differential equations (PDEs) that can be exponentially stabilized using backstepping controllers. For implementation, a finite-dimensional controller is generally needed. The backstepping controllers are approximated and it is proven that the finite-dimensional approximated controller stabilizes the original system if the order is high enough. This approach is known as late-lumping. The other approach to controller design for PDEs first approximates the PDE and then a controller is designed; this is known as early-lumping. Simulation results comparing the performance of late-lumping and early-lumping controllers are provided.enAttribution-NonCommercial-NoDerivatives 4.0 Internationalpartial differential equationsstabilizationbacksteppinglate-lumpingArticle