Fault Detection for Fuzzy Semi-Markov Jump Systems Based on Interval Type-2 Fuzzy Approach

Abstract

This article studies the fault detection problem for continuous-time fuzzy semi-Markov jump systems (FSMJSs) by employing an interval type-2 (IT2) fuzzy approach. First, the continuous-time FSMJSs model is designed and the parameter uncertainty is addressed by the IT2 fuzzy approach, where the characteristic of sensor saturation is taken into account in the control system. Second, the IT2 fuzzy semi-Markov mode-dependent filter is constructed, which is employed to deal with the fault detection problem. Then, by using the Lyapunov theory, it can be guaranteed that the constructed fault detection model based on this filter and IT2 FSMJSs is stochastically stable with H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance. Moreover, the quantization strategy is applied to the fault detection plant to dispose of the problem of limited network bandwidth. Compared with the existing literature, the differences mainly lie in two aspects, one is that the IT2 fuzzy method is utilized for FSMJSs to tackle the parameter uncertainty of system, and the other is to detect the fault signal of IT2 FSMJSs by using the fault detection system that is constructed based on the IT2 fuzzy semi-Markov mode-dependent filter and IT2 FSMJSs. Finally, two simulation examples are provided to illustrate the effectiveness and the usefulness of the proposed theoretical method.