2013/04/29 by Sylvain Ervedoza, Enrique Zuazua, Ervedoza, Sylvain +1
Engineering · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Control Systems and Identification #FOS: Mathematics #Model Reduction and Neural Networks #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems #math.AP #math.OC
paper · pdf · doi:10.48550/arxiv.1304.7749
arxiv created 2013/04/29 · openalex publication_date 2013/04/29 · arxiv updated 2013/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we consider abstract linear conservative systems and their time-discrete counterparts. Our main result is a representation formula expressing solutions of the continuous model through the solution of the corresponding time-discrete one. As an application, we show how observability properties for the time continuous model yield uniform (with respect to the time-step) observability results for its time-discrete approximation counterparts, provided the initial data are suitably filtered. The main output of this approach is the estimate on the time under which we can guarantee uniform observability for the time-discrete models. Besides, using a reverse representation formula, we also prove that this estimate on the time of uniform observability for the time-discrete models is sharp. We then conclude with some general comments and open problems.