A robust adaptive backstepping approach is considered in this paper to design excitation controllers for synchronous generators in power systems. The higher-order dynamical models of synchronous generators are considered to design the proposed excitation controller. Since the parameters appearing within these dynamical models (especially the parameters related to the synchronous generators and excitation systems) significantly affect the stability of power systems, these parameters are considered as completely unknown during the proposed controller design process. The parameter adaptation laws are used in this paper to estimate the unknown parameters while maintaining the overall stability of power systems. The effects of external disturbances are also considered in this paper to incorporate the model accuracies and measurement noises, which in turn ensure the robustness of the proposed control scheme. The control Lyapunov functions are used to analyze the stability of the whole system through the negative semi-definiteness of their derivatives. Simulation studies are carried out on an IEEE standard power system, the New England 10-machine 39-bus power system, to further validate the performance of the proposed scheme under different operating conditions. Comparisons are also made with different existing nonlinear excitation controllers sliding mode controller and robust partial feedback linearizing controller, which are designed based on the higher order models as well as with the robust adaptive controller, which is designed based on the traditional one-axis model. Simulations results, under different operating conditions, demonstrate the superiority of the proposed control scheme over all these existing nonlinear excitation controllers.