Stability analysis of feedback linearized magnetic levitation system using sum-of-squares method

Abstract

This study proposes the stability analysis of Magnetic Levitation System having a nonlinear controller, designed with feedback linearization based on the back-stepping method, using Sum of Squares (SOS) technique. The selection of Lyapunov function for nonlinear polynomial systems can be formulated as a convex optimization problem with the advancement of sum of squares method in the past few years. For this, the nonlinear systems with non-polynomial form are required to be recast into polynomial form first. This recasting results in increasing the order of the system.