A new approach using differential geometric theory to nonlinear control design for dual-excited synchronous generators is presented in this paper. As an example, a novel rotor angle and voltage stabilizing nonlinear optimal excitation control law of dual-excited synchronous generators is obtained, which is based on coordinate transformers and state feedback linearization combined with dynamic system. The computer simulation results on a single-machine infinite-bus power system show that dual-excited synchronous generator with proposed controller can improve dynamic stability and transient stability of power system to a great extent and has better dynamic characteristics than conventional synchronous generator.