Functional observers with linear error dynamics for discrete-time nonlinear systems, with application to fault diagnosis

TL;DR

This paper develops conditions for designing linear functional observers for discrete-time nonlinear systems, enabling efficient state estimation and fault diagnosis, with validation on a chemical reactor case study.

Contribution

It introduces necessary and sufficient conditions for lower order linear functional observers in discrete nonlinear systems, generalizing Luenberger's theory.

Findings

Derived conditions for observer existence

Validated on a chemical reactor case study

Demonstrated effectiveness for fault diagnosis

Abstract

This work deals with the problem of designing observers for the estimation of a single function of the states for discrete-time nonlinear systems. Necessary and sufficient conditions for the existence of lower order functional observers with linear dynamics and linear output map are derived. The results provide a direct generalization to Luenberger's linear theory of functional observers. The design methodology is tested on a non-isothermal CSTR case study.