Rational observers of rational systems

TL;DR

This paper presents a method for constructing rational observers for rational systems, involving a synthesis procedure that uses output-based realization and perturbation techniques, with examples demonstrating the approach.

Contribution

It introduces a systematic synthesis procedure for rational observers, linking algebraic observability to the existence of output-based rational realizations.

Findings

Finite algebraic observability implies existence of rational realization.

Constructed rational observers can have lower state-space dimension than polynomial observers.

Examples demonstrate the effectiveness of the proposed observer synthesis.

Abstract

Rational observers are to be constructed for rational systems while polynomial observers are to be constructed for polynomial systems. An observer synthesis procedure is formulated. First an output-based rational realization is synthesized for the considered rational system. Then a perturbation technique creates an observer. Finite algebraic observability of the rational system impies the existence of a output-based rational realization. Several examples of rational observers are provided including a polynomial system of which the state-space dimension of the polynomial observer is strictly higher than that of the corresponding system.