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This paper proposes a methodology to design a robust observer for Takagi–Sugeno descriptor (TS-D) systems with unmeasurable premise variables and its application to sensor fault detection and isolation. A robust H_∞ approach is considered to minimize the effect of uncertainties given by the unmeasurable premise variables, disturbances and sensor noise. As a result, a set of relaxed linear matrix inequalities (LMI) are derived, which provides sufficient conditions to guarantee the convergence of the proposed state observer. Finally, a conventional fault detection scheme is considered by means of residual generation and evaluation. An academic example is given to illustrate the effectiveness of the proposed method.