Actuator and sensor fault estimation for T–S fuzzy fractional-order systems based on adaptive and sliding mode observers

This study delves into the issue of estimating faults in actuators and sensors for a specific category of uncertain fractional-order nonlinear systems (FONSs). This category is characterized by Takagi-Sugeno (T-S) fuzzy model, which operates in the presence of local nonlinear functions and external disturbances. The fractional-order T-S fuzzy system is divided into two subsystems using linear coordinate transformations: The first subsystem includes the effects of disturbances but not sensor faults, while the second subsystem incorporates sensor faults but no disturbances. Subsequently, a T-S fuzzy fractional sliding mode observer (FSMO) is constructed based on the first subsystem to entirely neutralize the impact completely of external disturbances. For the second subsystem, a T-S fuzzy fractional adaptive observer (FAO) is formulates to estimate both actuator and sensor faults, leveraging the estimated output subsystem. The stability analysis of state estimation errors ventures into the domain of Lyapunov stability theory for FONSs, thereby enriching our comprehension of their dynamics and predictive abilities. The necessary conditions for stability are subsequently deduced and articulated in the form of linear matrix inequalities (LMIs). To corroborate the findings, an exemplifying scenario is demonstrated at the end. AMS Subject Classifications : 34K20.