Robust fault diagnosis of fractional order Takagi–Sugeno systems with uncertainties in premise variables

This paper introduces two novel fault detection techniques employing Fractional Order Proportional Integral Fuzzy Observer (FO-PIFO) designs to diagnose nonlinear systems modeled by Fractional Order Takagi-Sugeno (FO-TS) frameworks. The proposed approaches address both measurable premise variables (MPV) and unmeasurable premise variables (UPV), facilitating the development of observer banks for effective fault detection. By extending prior research, largely limited to integer-order Takagi-Sugeno models, into the domain of fractional-order systems, this study fills a critical gap in the literature. Two strategies are proposed to ensure compatibility with fractional-order modeling: one reformulates FO-TS models using MPV, while the other constructs FO-TS models with UPV via uncertain fuzzy models incorporating approximated states. The FO-PIFO convergence criteria are derived using fractional-order Lyapunov theory, and the associated stability conditions are expressed as Linear Matrix Inequalities (LMIs). To enhance robustness, strategies for mitigating external disturbances are also integrated. The resulting FO-PIFO designs are then employed to build observer banks that generate residuals for detecting actuator and sensor faults. Finally, multiple simulation scenarios are presented to validate the effectiveness and practicality of the proposed diagnostic methods.