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 =H1 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.