PreprintCC BY 4.0arXiv
Global L1 Exponential Observer for the Quasilinear Diffusion Equation
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 L1 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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BibTeX
@misc{belhadjoudja2026global,
title = {{Global $L^1$ Exponential Observer for the Quasilinear Diffusion Equation}},
author = {Mohamed Camil Belhadjoudja and Kirsten Morris},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06546},
eprint = {2610.06546},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06546},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Global L^1 Exponential Observer for the Quasilinear Diffusion Equation
AU - Mohamed Camil Belhadjoudja
AU - Kirsten Morris
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06546
UR - https://arxiv.org/abs/2610.06546
AB - 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.
ER -