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.

对于用热 PDE 传感器观察的线性植物，解决了观察器设计问题，从而产生了具有 ODE-PDE 级联结构的全局系统。该研究的一个新颖之处在于 PDE 传感器包括全局 Lipschitz 非线性动力学。另一个新颖之处在于，所提出的观察器依赖于传感器边界处的采样测量。观察者提供工厂（有限维）状态向量和传感器 PDE 分布状态的在线估计。观测误差系统的指数稳定性使用类反推变换、Lyapunov-Krasovski 型泛函、Wirtinger 和 Halanay 不等式进行分析。模拟结果突出了其他观察者特征，包括其对全局 Lipschitz 假设的鲁棒性，以及其对输出反馈稳定的适用性。