This paper presents an unknown input observer design method for a class of nonlinear systems in the presence of disturbances in both the systems dynamics and the output. The main motivation of this work is to develop a state estimator for PEM-Fuel Cell Stack systems. More precisely, the paper addresses the observation issue of the main variables of the fuel cell systems that are the compressor speed, the supply manifold pressure, the mass of the gas accumulated in the supply manifold volume, the partial pressure of oxygen and the partial pressure of nitrogen in the cathode channel. The proposed approach considers the current as an unknown input and uses the air flow rate through the compressor and the total pressure as measurements. By means of regular transformations, the Jacobian of the nonlinear functions and the convexity principle, the observer design problem is turned into a LMI feasibility problem. Simulation results with a refined model show the good convergence properties of the observer.Index Terms-Fuel cell stacks, H∞ performance, state and unknown input estimation, nonlinear observer, linear matrix inequalities.