Testing Backward-Flatness of Nonlinear Discrete-Time Systems

TL;DR

This paper introduces a systematic method for testing backward-flatness in nonlinear discrete-time systems, expanding the tools available for analyzing system flatness beyond the already efficiently testable forward-flatness.

Contribution

The paper proposes a new approach for testing backward-flatness and deriving backward-flat outputs, addressing a previously challenging problem in system flatness analysis.

Findings

A systematic testing method for backward-flatness is developed.

The relationship between Jacobian matrices of backward- and forward-flat systems is analyzed.

An academic example illustrates the proposed approach.

Abstract

Despite ongoing research, testing the flatness of discrete-time systems remains a challenging problem. To date, only the property of forward-flatness - a special case of difference-flatness - can be checked in a computationally efficient manner. In this paper, we propose a systematic approach for testing backward-flatness, which is another special case of difference-flatness, and for deriving a corresponding backward-flat output. Additionally, we discuss the relationship between the Jacobian matrices associated with the flat parameterization of backward- and forward-flat systems and illustrate our results by an academic example.