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This study provides a new method for non-linear robust adaptive excitation controller design for power systems. This method can be developed by using the back-stepping technique, but needs fewer conditions than the conventional methods, which is more desirable in power systems. This method is guaranteed to be robust in the presence of model errors and disturbances, and will adapt to uncertain parameters. Meanwhile, the over-parameterisation problem that usually appears in some adaptive methods is avoided. Simulations on a 4-machine-2-area power system and the East China power system demonstrate the effectiveness of the suggested method.