An Observable Canonical Form for a Rational System on a Variety

TL;DR

This paper develops an observable canonical form for single-input-single-output rational systems on a variety, ensuring a unique minimal realization based on their response maps, with proofs of its well-defined nature.

Contribution

It introduces a new canonical form for rational systems on a variety, extending the concept of observability to this class of systems.

Findings

The canonical form is well-defined and unique.

It applies to minimal realizations of response maps.

Special cases of the form are discussed.

Abstract

An observable canonical form is formulated for the set of rational systems on a variety each of which is a single-input-single-output, affine in the input, and a minimal realization of its response map. The equivalence relation for the canonical form is defined by the condition that two equivalent systems have the same response map. A proof is provided that the defined form is well-defined canonical form. Special cases are discussed.