Almost Feedback Linearization via Dynamic Extension: a Paradigm for Robust Semiglobal Stabilization of Nonlinear MIMO Systems

It is well known that invertible MIMO nonlinear systems, can be input–output linearized via dynamic state feedback (augmentation of the dynamics and memoryless state feedback from the augmented state). The procedures for the design of such feedback, developed in the late 1980s for nonlinear systems, typically are recursive procedures that involve state-dependent transformations in the input space and cancelation of nonlinear terms. As such, they are fragile. In a recent work of Wu-Isidori-Lu-Khalil, a method has been proposed, consisting of interlaced design of dynamic extensions and extended observers, that provides a robust version of those feedback-linearizing procedures. The method in question can be used as a systematic tool for robust semiglobal stabilization of invertible and strongly minimum-phase MIMO nonlinear systems. The present paper provides a review of the method in question, with an application to the design of a robust output regulator.