This paper investigates the fault detection problem for nonlinear parabolic PDE systems. In contrast to the existing works, the designed fault detection observer utilizes less state information in both time domain and space domain, the details of which are illustrated as follows. First, based on Takagi–Sugeno fuzzy theory, a novel fuzzy state observer is developed via sampling in time and space approach. Then, by using Lyapunov direct method, some sufficient conditions that guarantee both the disturbance/control-inputs attenuation performance and the faulty sensitivity performance of the fault detection systems are established in the form of linear matrix inequality, which provides an effective approach to optimize the systems’ performance. Finally, two simulation examples are given to illustrate the effectiveness of the designed fault detection systems.

本文研究了非线性抛物线PDE系统的故障检测问题。与现有工作相反，设计的故障检测观察器在时域和空域中利用的状态信息较少，其详细信息如下所示。首先，基于Takagi–Sugeno模糊理论，通过时空采样方法开发了一种新型的模糊状态观测器。然后，利用李雅普诺夫直接法，以线性矩阵不等式的形式建立了同时保证故障检测系统的扰动/控制输入衰减性能和故障灵敏度性能的充分条件，为优化系统的优化设计提供了有效的途径。系统的性能。最后，