A new way for robustness analysis of nonlinear control systems: Application to a magnetic suspension device

The stability robustness analysis for a class of nonlinear systems with bounded structured uncertainties is characterized by Nonlinear Matrix Inequalities (NLMI). By introducing scaling to reduce conservatism arising from the uncertainty structure, the problem turns out to be still convex. However, it is shown that it is as hard as Lyapunov stability analysis. In this paper, it is proposed a new way for the stability robustness analysis. It consists of splitting the problem into two steps and treating it on the basis of Lyapunov designs. As application, we have applied the nonlinear backstepping based approach to deal with the problem of stabilizing a magnetic suspension system with bounded structured uncertainties. Numerical simulations as well as experimental results have been performed, they are shown to be satisfactory and are in concordance.