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The problem of observer design is addressed for linear plants that are observed with heat PDE sensors, leading to a global system with ODE-PDE cascade structure. One novelty of the study is that the PDE sensor includes globally Lipschitz nonlinear dynamics. The other novelty is that the proposed observer relies on sampled measurements at the sensor boundary. The observer provides online estimates of both the plant (finite-dimensional) state vector and the sensor PDE distributed state. Exponential stability of the observation error system is analysed using backstepping-like transformation, Lyapunov-Krasovski type functional, Wirtinger’s and Halanay’s inequalities. Additional observer features are highlighted by simulation results, including its robustness to global Lipschitz assumption, and its applicability to output feedback stabilisation.

Sampled-output observer design in the presence of nonlinear heat PDE sensor