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The fuel cell oxygen starvation problem is addressed in this paper using a robust load governor. By regulating the current drawn from the fuel cell, the pointwise-in-time constraints on the oxygen excess ratio and on the oxygen mass inside the cathode are strictly enforced to protect the fuel cells from oxygen starvation. The load governor is designed using a nonlinear reference governor approach. Parameter uncertainties such as those due to imperfect controls of temperature and humidity are handled in the load governor design using a novel approach based on sensitivity functions. Simulation results are included to demonstrate the effectiveness of the proposed scheme. The results are compared with those of a linear filter which has been proposed in the prior literature to achieve similar goals.