In this brief, we present Lyapunov-based robust and adaptive higher order sliding mode (HOSM) controllers for the air-feed system of polymer electrolyte membrane fuel cells, which is a nonlinear single-input, single-output system with bounded uncertainty. The system consists of a motorized compressor, which is driven at its optimal point in order to minimize the internal energy consumption of the system. This brief provides an experimental demonstration of the applicability of the recently developed fixed-gain robust controller and adaptive controller for this problem. Third-order controllers are developed in order to obtain a continuous profile for the input current of the compressor motor. In this regard, a complete adaptive arbitrary HOSM control has been presented for the first time, with Lyapunov-based proof. A performance comparison between the two controllers is presented in the end.