In this paper, an algebraic-observer-based output-feedback controller is proposed for a Proton Exchange Membrane Fuel Cell (PEMFC) air-supply subsystem, based on both algebraic differentiation and sliding-mode control approaches. The goal of the design is to regulate the Oxygen Excess Ratio (OER) towards its optimal setpoint value in the PEMFC air-supply subsystem. Hence, an algebraic estimation approach is used to reconstruct the OER based on a robust differentiation method. The proposed observer is known by its finite-time convergence and low computational time compared to other observers presented in the literature. Then, a twisting controller is designed to control the OER by manipulating the compressor motor voltage. The parameters of the twisting controller have been calculated by means of an off-line tuning procedure. The performance of the proposed algebraic-observer-based output-feedback controller is analyzed through simulations for different stack-current changes, for parameter uncertainties and for noise rejection. Results show that the proposed approach properly estimates and regulates the OER in finite-time.IET Research Journals, pp. 1-8 c The Institution of Engineering and Technology 2015 the OER in Section 4. Different simulation scenarios, including performance results, parameter uncertainties, noise in measurement and comparison study, are discussed in Section 5. Finally, the major conclusions are presented in Section 6.