Diagnostic observer-based fault detection for nonlinear parabolic PDE systems via dual sampling approaches

Abstract

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.