Asynchronous Fault Detection for Interval Type-2 Fuzzy Nonhomogeneous Higher-level Markov Jump Systems with Uncertain Transition Probabilities

Abstract

Based on the interval type-2 fuzzy (IT2F) approach, this paper investigates the fault detection filter design problem for a class of nonhomogeneous higher-level Markov jump systems with uncertain transition probabilities. Considering that the mode information of the system cannot be obtained synchronously by the filter, the hidden Markov model can be seen as a detector to handle this asynchronous problem, and the parameter uncertainty can be processed by the IT2F approach with the lower and upper membership functions. Then, the asynchronous IT2F filter is designed to deal with the fault detection problem. Furthermore, the Gaussian transition probability density function is introduced to describe the uncertainty transition probabilities of the system and the filter. Based on Lyapunov theory, the existence of the designed asynchronous IT2F filter and the dissipativity of the filter error system can be well ensured. The simulation study on a quarter-car suspension system verifies that the designed asynchronous IT2F filter can detect faults without error alarms.