Multi‐objectiveH− ∕ H∞fault detection observer design for Takagi–Sugeno fuzzy systems with unmeasurable premise variables: descriptor approach

SUMMARY This paper investigates the problem of robust fault detection observer design for nonlinear Takagi–Sugeno models with unmeasurable premise variables subject to sensor faults and unknown bounded disturbance. The main idea is to synthesize a robust fault detection observer by means of a mixed H − ∕ H ∞ performance index. The considered observer is used to estimate jointly states and faults. Using the technique of descriptor system representation, we proposed a new less‐conservative approach in term of a linear matrix inequality (LMI) by considering the sensor fault as an auxiliary state variable. A solution of the problem is obtained by using an iterative LMI procedure.