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This paper extends a newly developed adaptive back-stepping algorithm for systems in parametric feedback form to general nonlinear systems. The extended method is applied to robust nonlinear design of excitation control of power systems containing some unknown parameters. The proposed method differs from the "classical" adaptive back-stepping design in the way the parameter estimator is constructed and in the way the nonlinear gains are assigned. Simulation results compared with the "classical" adaptive back-stepping method on a single-machine infinite bus system (SMIB) demonstrate that this proposed controller can obtain better performances. In addition, this extended algorithm is applicable to other control systems.