Homogeneous Approximation, Recursive Observer Design, and Output Feedback

TL;DR

This paper introduces two novel tools for nonlinear observer and output feedback design: a bi-limit homogeneous approximation and a recursive observer, leading to new global stabilization results.

Contribution

It presents a bi-limit homogeneous approximation extension and a recursive observer design, enabling improved output feedback stabilization for nonlinear systems.

Findings

Homogeneity in the bi-limit enhances stability analysis.

Recursive observer design simplifies nonlinear observer construction.

New global stabilization results for feedback systems.

Abstract

We introduce two new tools that can be useful in nonlinear observer and output feedback design. The first one is a simple extension of the notion of homogeneous approximation to make it valid both at the origin and at infinity (homogeneity in the bi-limit). Exploiting this extension, we give several results concerning stability and robustness for a homogeneous in the bi-limit vector field. The second tool is a new recursive observer design procedure for a chain of integrator. Combining these two tools, we propose a new global asymptotic stabilization result by output feedback for feedback and feedforward systems.