Stubborn Observers for Infinite-dimensional Systems in Abstract Form with Application to Parabolic PDEs with Boundary Measurement
Résumé
Building upon the recently developed "stubborn" observer construction for finite-dimensional systems, we present a novel observer structure for abstract linear infinite-dimensional systems. 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 the input-tostate stability (ISS) of the error system in the presence of measurement disturbances but also demonstrates significant resilience to impulsive noise. We illustrate the effectiveness of our method by applying it to a class of parabolic partial differential equations (PDEs).
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