25 mars 2026 à 13h30
Building upon the recently developed stubborn observer construction for finite-dimensional systems, we present a novel observer structure for linear infinite-dimensional systems in abstract form. A key feature of our design is the use of nonlinear output injection terms with an adjustable dynamical saturation function. This approach not only ensures input-to-state stability (ISS) for the error system in the presence of measurement disturbances but also demonstrates significant resilience to impulsive noise. This latter feature represents a significant improvement over existing results, where impulsive noise can degrade observer performance, lead to instability, or cause the violation of critical physical constraints. The effectiveness of our method is demonstrated through a class of parabolic partial differential equations (PDEs).
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