On the robustness of feedback linearization

Feedback linearization is possibly the most widely used technique for controlling nonlinear systems without resorting to local linearization. In this algorithm the system nonlinearities are canceled by the control input, but accurate cancelation requires a precise modeling of the system. The possibility that an exact cancelation may not occur as a consequence of modeling errors has raised justifiable concerns about the robustness of this methodology and feedback linearization is widely cited in the literature as a non-robust design technique. This paper examines the robustness—or lack thereof—of the feedback linearization methodology and introduces two methodologies that provide clear guidelines on how to design a feedback linearized controller that is stable in the presence of Lipschitz bounded uncertainties. It is shown that a feedback linearized controller can be designed to be robust in face of parametric uncertainties, by simply pushing the closed-loop eigenvalues far enough to the left in the complex plane if the eigenvalues are sufficiently far apart. For structural uncertainties, such a strong result could not be obtained in general. Examples of stable feedback linearization of uncertain nonlinear dynamics are presented at the end.