Robust Feedback Linearization for Full Relative Degree Input-Affine Nonlinear Systems

Feedback linearization generally implies exact knowledge of the dynamical model of a nonlinear input-affine process. This is an inherent limitation of the method in its current use in the literature, as models are only partially known, with the remaining unknown dynamics considered as uncertainties. The purpose of this paper is to consider the full relative degree case and determine conditions to ensure asymptotic stability for the entire family of processes by employing the nominal nonlinear model and an uncertain linear block. The resulting linear inverse additive uncertainty model always leads to an improper descriptor system which can be fit from frequency response data through a proposed algorithm. A numerical case study further illustrates this approach.