Functional Observers with Linear Error Dynamics for Nonlinear Systems

TL;DR

This paper develops a framework for designing functional observers with linear error dynamics for nonlinear systems, generalizing classical linear observer theory to nonlinear contexts.

Contribution

It introduces conditions for lower-order linear functional observers in nonlinear systems, extending Luenberger's linear observer theory.

Findings

Necessary and sufficient conditions for existence of linear functional observers.

Formulation of functional observer linearization in nonlinear systems.

Generalization of linear observer theory to nonlinear dynamics.

Abstract

In this work, the problem of designing observers for estimating a single nonlinear functional of the state is formulated for general nonlinear systems. Notions of functional observer linearization are also formulated, in terms achieving exactly linear error dynamics in transformed coordinates and with prescribed rate of decay of the error. Necessary and sufficient conditions for the existence of a lower-order functional observer with linear dynamics are derived. The results provide a direct generalization of Luenberger's linear theory of functional observers to nonlinear systems.