Abstract: A new robust fault diagnosis method based Oil linear matrix inequality (LMI) for non-linear difference-algebraic systems (DAS) with uncertainties is proposed. Based on the known nominal model of DAS, an auxiliary system consisting of a difference equation and an algebraic equation is firstly constructed. Then, based on the relationship between the state deviation and the faults in the difference equation and the relationship between the algebraic Variable deviation and the faults in algebraic equation, the problem of fault identification is converted into the problem of parameter estimation. Finally fault identification is realized using LMI method. Simulation results show the effectiveness of the presented method.