Exponential H^1 stability of the observation error is shown for the quasilinear heat equation using linear backstepping design, with convergence to zero despite persistent mismatch and a non-monotonic gain-rate relationship.
Boussinesq, Recherches th´ eoriques sur l’´ ecoulement des nappes d’eau infiltr´ ees dans le sol et sur le d´ ebit des sources, Journal de Math
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Backstepping Observer for the Quasilinear Heat Equation with Linear Design Gains: Beyond Local Stability
Exponential H^1 stability of the observation error is shown for the quasilinear heat equation using linear backstepping design, with convergence to zero despite persistent mismatch and a non-monotonic gain-rate relationship.