In this paper, we present some results obtained from the application of a class of sliding mode observers to the model-based fault diagnosis problem in non-linear dynamic systems. A Takagi-Sugeno fuzzy model is used to describe the system and then sliding mode observers are designed to estimate the system state vector, from this the diagnostic signal-residual, is generated by the comparison of measured and estimated output. The linear integer programming technique is proposed to solve the fault isolation problem based in signal-residual. The proposed technique allows determinating the faulted component corresponding to the active signal-residual. This paper shows an application of the fault diagnosis technique which was tested satisfactorily in a two-tank hydraulic system.