Observer-based fuzzy fault-tolerant control for nonlinear systems in the presence of general noise

This paper focuses on the observer-based fuzzy fault-tolerant control problem for nonlinear systems with general noise. The fault of component and general noise can greatly change the behavior of the system, resulting in system instability. Stochastic differential equations theory, as an effective tool, can deal with the control problem of interval type-2 (IT2) Takagi–Sugeno (T-S) fuzzy systems influenced by white noise. However, compared with stochastic differential equations, random differential equations are more effective under the condition that random disturbances must be described by stationary processes rather than by white noise. In this paper, by using mixed design method based on interval type-1 (IT1) observer and IT2 controller, the problem of observer-based fault-tolerant control for nonlinear systems with general noise is solved. Moreover, considering the use of general noise to describe the effects of stationary processes on the system and by virtue of random differential equation theory, the noise-to-state stability in probability (NSS-P) of considered system is analyzed and the LMIs-based stability criteria are obtained in observer design process. Similar results can also be obtained in the controller design process. The proposed method not only reduces the computational burden of designing observer-based fault-tolerant controller, but also gives the result with lower conservatism. It means that the proposed method can deal with greater uncertainty. Finally, the effectiveness of the proposed method has been verified according to the example.