Fault Detection for Uncertain Polynomial Fuzzy Systems Using $H_{-}/L_{\infty }$ Observer and Ellipsoidal Analysis

This article investigates the fault detection problem of polynomial fuzzy systems with parameter uncertainty, external disturbance, and measurement noise. Based on the $H_{-}/L_{\infty }$ observer and ellipsoidal analysis, a fault detection observer is designed, which is sensitive to faults while robust to disturbances. By using the given $H_{-}$ and $L_{\infty }$ performance indexes, the design conditions of fault detection observer are derived in sum of squares. The $H_{-}/L_{\infty }$ fault detection observer can generate the residual for fault detection. We consider the fault-free condition that the admissible residual values are contained in compact sets. Based on the generated residual, the ellipsoidal analysis is used to evaluate the residual and detect the fault. Finally, the feasibility and effectiveness are verified through the simulation of a numerical nonlinear model.