Observer-based output-feedback stabilization of continua of linear hyperbolic PDEs using backsteppingObserver-based output-feedback stabilization of continua of linear hyperbolic PDEs using backstepping Πλήρης Δημοσίευση σε Συνέδριο Conference Full Paper 2025-09-032025enWe develop a boundary observer design for a class of continua of linear hyperbolic PDE systems, which are viewed as the continuum version of n + m general heterodirectional hyperbolic systems as n to ∞. The design relies on the introduction of a novel, continuum PDE backstepping transformation, which enables the construction of a Lyapunov functional for the estimation error system. We then introduce the respective non-collocated, output-feedback design employing the stabilizing continuum control kernels from Humaloja and Bekiaris-Liberis [2024]. (The observer-based output-feedback stabilization problem for the class of ∞ + 1 hyperbolic systems can be solved as special case of the design procedure presented here.) Stability under the observer-based output-feedback law is established by using the Lyapunov functional construction for the estimation error system and proving well-posedness of the complete closed-loop system, which allows utilization of the separation principle. We illustrate the output-feedback design in simulation, via a numerical example for which the control and observer kernels can be computed in closed form.Funded by the European Union (ERC, C-NORA, 101088147). Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them.http://creativecommons.org/licenses/by-nc-nd/4.0/5th IFAC Workshop on Control of Systems Governed by Partial Differential Equations - CPDE 2025Humaloja_et_al_IFAC_CPDE 2025_preprint.pdfChania [Greece]Library of TUC2025-09-02application/pdf348.0 kB10.1016/j.ifacol.2025.08.081free Humaloja Jukka-Pekka Gabriel Humaloja Jukka-Pekka-Gabriel Bekiaris-Liberis Nikolaos Μπεκιαρης-Λυμπερης Νικολαος PDE Continua Hyperbolic PDEs Backstepping Observer Output Feedback