Robust Asymptotic Stabilization of Nonlinear Systems with Non-Hyperbolic Zero Dynamics

TL;DR

This paper introduces a new method for stabilizing nonlinear systems with zero dynamics that are asymptotically stable but not exponentially, using output feedback without relying on observers or separation principles.

Contribution

It provides a novel stabilization approach for nonlinear systems with non-hyperbolic zero dynamics, based on partial detectability and nonlinear internal models.

Findings

Design of locally Lipschitz stabilizers under partial detectability.

A robust stabilization paradigm independent of observer design.

Application of nonlinear internal models to stabilization.

Abstract

In this paper we present a general tool to handle the presence of zero dynamics which are asymptotically but not locally exponentially stable in problems of robust nonlinear stabilization by output feedback. We show how it is possible to design locally Lipschitz stabilizers under conditions which only rely upon a partial detectability assumption on the controlled plant, by obtaining a robust stabilizing paradigm which is not based on design of observers and separation principles. The main design idea comes from recent achievements in the field of output regulation and specifically in the design of nonlinear internal models.