Backstepping Time-scale Separation Redesign for Stabilization of a Class of Nonlinear Systems with Matched and Unmatched Uncertainties

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 backsteppingmethod. Based on Lyapunov stability theorem, sufficient conditions for stabilization of the output of the system areachieved. To deal with the existence of uncertainties, high-gainfilters are designed, which estimate the uncertainties, using singular perturbation theory. Finally, a numerical simulation ispresented to show the effectiveness of the proposed control scheme.

Keywords:

Nonlinear control , time-scale separation , unmatched uncertainty , backstepping