Stabilization of Uncertain Systems using Backstepping and Lyapunov Redesign

This article presents stabilization method for uncertain system using backstepping technique and Lyapunov redesign. The design begins by obtaining stabilizing function for unperturbed system using control Lyapunov function. As such, the stabilizing function guarantees asymptotic stability in the sense of Lyapunov. The control Lyapunov function is re-used in the re-design phase whereby the nonlinear robust function is then augmented with pre-designed stabilizing function for robustness toward uncertainties. Lyapunov redesign is used in designing overall robust stabilizing function which guarantees asymptotic stability toward uncertainties and also toward any perturbed states within asymptotic stability region.