Abstract
The extension of the backstepping-based state observer design is considered for general periodic quasi-linear parabolic PDEs in one space dimension. Here, the extended linearization combined with a suitable coordinate and state transformation is employed. This allows for the application of the backstepping method for the determination of an extended Luenberger observer with observer gains entering the PDE and the boundary condition which ensures an exponential decay of the linearized observer error dynamics. This is confirmed analytically, while the convergence of the quasi-linear observer error system is studied in numerical simulations.
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