Summary: In order to improve the asymptotic stability for a kind of nonlinear systems with unmatched uncertainties and simplify the calculation of back-stepping adaptive sliding mode control, by adopting additional control input, the level of the subsystem virtual function designment difficulty is reduced, the asymptotic stabilization of the state variables is realized, which can not be resolved using the traditional back-stepping adaptive L2-gain control method while the upper bound of the interference need not to be considered, and the common formulas of the back-stepping adaptive sliding mode robust control with additional control input (BASMRC-ACI) is deduced. In order to test the performance of the proposed control method, taking the type harmonic excitation system for example, simulation experiments are performed in load increasing and ground fault states. Simulation results show that by the BASMRC-ACI, comparing with the back-stepping adaptive L2-gain control method, the asymptotic stability rate of the excitation system state variables is enhanced, overshoot is reduced and the convergence speed is improved, which are important for enhancing the dynamic stability of the harmonic excitation system.