Event-based fuzzy fault detection for stochastic nonlinear parabolic PDE system with Markovian jumping faults

This paper investigates the fault detection problem for a class of semi-linear partial differential equation (PDE) systems. Specifically, the complexities of the studied system, that is, nonlinearity, stochasticity and external disturbance, are considered and reconstructed as the Takagi-Sugeno (T-S) fuzzy model. The primary purpose of this paper is to construct a fuzzy asynchronous fault detection filter for detecting the random fault signals that can be described by a Markov process. In particular, to save network transmission resources, an adaptive event-triggered mechanism (AETM) can be employed to dynamically select the triggered signal by designing an adaptive threshold before the input signal is transmitted to the filter. Furthermore, by applying the Lyapunov stability theory, the stochastic theory and several inequality transformation techniques, sufficient conditions are obtained for the asymptotic stability of the augmented system in the form of linear matrix inequality, and the desired filter’s parameters can be obtained in explicit form. A high-speed aerospace fin temperature distribution model is presented to illustrate the effectiveness of the described scheme by comparisons.