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This paper addresses the problem of fault detection and isolation (FDI) for a class of Lipschitz nonlinear systems with unknown inputs. We propose two new approaches based on unknown input observer design technique to detect, locate and estimate additional faults. The observer design problem is formulated in Linear Matrix Inequalities (LMI) terms which can be solved easily using LMI technique. An application of quadruple-tank process is presented to show the performance of the proposed approaches.