Backstepping time-scale separation redesign for stabilization of a class of nonlinear systems with matched and unmatched uncertainties

摘要

In this paper, a state-feedback controller is proposed for stabilization of a class of nonlinear systems in the presence of matched and unmatched uncertainties via backstepping method. Based on Lyapunov stability theorem, sufficient conditions for stabilization of the output of the system are achieved. To deal with the existence of uncertainties, high-gain filters are designed, which estimate the uncertainties, using singular perturbation theory. Finally, a numerical simulation is presented to show the effectiveness of the proposed control scheme.