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 1 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.In the field of diagnosis, this assumption forces to design observers with weighting functions depending on the input u.t /, for the detection of the sensors faults, and on the output y.t /, for the detection of actuator faults. Indeed, if the decision variables are the inputs, for example, in a bank of observer, even if the i th observer is not controlled by the input u i , this input appears indirectly in the weighting function and it cannot be eliminated. For this reason, it is interesting to consider the case of weighting functions depending on unmeasurable premise variables, such as the state of the system. This case makes it possible to handle a large class of physical systems [21][22][23].Using descriptor approach, this work dealt with the problem of fault detection observer for Takagi-Sugeno (T-S) model affected by both sensor faults and bounded disturbances. Although many papers have dealt with the problem of observer design for descriptor systems, only a few works have been carried out for simultaneous disturbance rejection and fault detection algorithms [1]. Compared with existing fault estimation schemes [24,25], the given descriptor observer approach leads to more suitable observer design, which is applicable to diagnosis of more general faults. The proposed procedure has the advantage, over the ones proposed on [26,27], to estimate different faults types, whereas the proposed method in [26] is only able to estimate step faults. The problem formulation in a descriptor form allows also to estimate state and sensor faults simultaneously.This paper aims to extend the results proposed in [4] to T-S models with unmeasurable premise variables. The present work illustrates the design of a fault detection observer for T-S model affected by sensor faults and unknown bounded disturbances. The observer gains and the residual weighting matrix are obtained through the minimization of an H 1 norm and the maximization of an H norm. The main objective is to design a fault detection observer such that the resulting residual has the best robustness to disturbances and the best sensitivity to faults. Sufficient conditions are expressed in terms of linear matrix inequalities (LMIs), and an iterative algorithm is provided to get the solution. This algorithm can be solved effectively using numerical optimization techniques.This paper is organized as follows. In ...