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A hybrid solid oxide fuel cell and gas turbine (SOFC/GT) system exploits the complementary features of the two power plants, where the GT recuperates the energy in the SOFC exhaust stream and thereby boosting the overall system efficiency. Through model based transient analysis, however, it is shown that the intricate coupling dynamics make the transient load following very challenging. Power shutdown has been observed when the load is changed abruptly in the generator. In this work, a novel closed-loop reference governor controller is proposed to mitigate the shutdown phenomenon. The reference governor utilizes the region of attraction of a reduced order SOFC/GT model to determine if an incremental step change is allowable, i.e., it does not cause a shutdown. It is shown that with a moderate computational cost, the speed of the hybrid power system response can be improved significantly compared to the fastest conventional load filter. Several design parameters, such as the sampling rate and incremental step-size, are also explored to understand the trade-offs between computational complexity and performance improvement.