There exists a large class of nonlinear systems with uncertainties, such as hydraulic turbine governors, whose robust control problem is hard to solve by means of the existing robust control approaches. For this class of systems, this work presents a dynamic extending H∞ controller via both differential geometry and H∞ theory. Furthermore, based on differential game theory, it has been verified that the proposed control strategy has robustness in the sense that the disturbance can be attenuated effectively because the L2-gain from the disturbance input to the regulation output signal could be reduced to any given level. Thirdly, a robust control strategy for hydraulic turbine governor is designed according to the proposed extending H∞ control method, and has been developed into a real control equipment. Finally the field experiments are carried out which show clearly that the developed control equipment can enhance transient stability of power systems more effectively than the conventional controller.