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arXiv · 2610.06546

Global $L^1$ Exponential Observer for the Quasilinear Diffusion Equation

Mohamed Camil Belhadjoudja·Kirsten Morris
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Abstract

A nonlinear observer is designed for a one-dimensional quasilinear diffusion equation with Neumann boundary conditions, using as an output the state at one end of the spatial domain. The observer consists of a copy of the system, with a nonlinear (in the output) correction term at the boundary. A Lyapunov-based analysis is performed to ensure global exponential stability of the zero equilibrium for the estimation error dynamics in the $L^1$ norm. The result holds for a general nonlinear diffusivity, under the assumption that it is lower-bounded by a positive constant, i.e., that the diffusion equation is uniformly parabolic.

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Mohamed Camil Belhadjoudja, Kirsten Morris. 2026-10-05. Global $L^1$ Exponential Observer for the Quasilinear Diffusion Equation. https://arxiv.org/abs/2610.06546

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