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This study proposes a feedback linearisation based on the back-stepping method with simple implementation and unique design process to design a non-linear controller with a goal of improving both steady-state and transient stability. The proposed method is designed based on a standard third-order model of synchronous generator. A comparison based on simulation is then performed between the proposed method and two conventional control schemes (i.e. conventional power system stabiliser and direct feedback linearisation). The simulation results demonstrate that fast response, robustness, damping, steady-state and transient stability as well as voltage regulation are all achieved satisfactorily.