Robust nonlinear control associating robust feedback linearization and H∞ control

In this note, a robust nonlinear controller for a nonlinear system subject to model uncertainties is proposed. Such a controller associates a "robust feedback linearization" with a robust linear H_∞ controller. The robust feedback linearization exactly transforms the nonlinear system into a linear system equal to the linear approximation of the original nonlinear system around a nominal operating point. The robustness of the resulting overall nonlinear controller is proved by theoretical arguments and illustrated through an application example, the control of a magnetic bearing system.