Duality of Geometric Tests for Forward-Flatness

TL;DR

This paper explores the duality between two geometric tests for forward-flatness in discrete-time systems, revealing their fundamental relationship and illustrating the concepts with an academic example.

Contribution

It demonstrates that the two geometric tests for forward-flatness are dual to each other and clarifies their relationship.

Findings

The two tests are mathematically dual.

The relation between involutive distributions and integrable codistributions is established.

Illustrative example demonstrates the duality concept.

Abstract

Recently it has been shown that the property of forward-flatness for discrete-time systems, which is a generalization of static feedback linearizability and a special case of a more general concept of flatness, can be checked by two different geometric tests. One is based on unique sequences of involutive distributions, while the other is based on a unique sequence of integrable codistributions. In this paper, the relation between these sequences is discussed and it is shown that the tests are in fact dual. The presented results are illustrated by an academic example.