Flatness of Two-Input Discrete-Time Systems and their Linearization

TL;DR

This paper investigates the flatness properties of two-input discrete-time nonlinear systems, establishing rank conditions for flatness subclasses and proposing a dynamic extension method for exact linearization.

Contribution

It introduces a general framework for flatness in discrete-time systems, relates rank conditions to subclasses, and proposes a simple dynamic extension for linearization.

Findings

Rank conditions characterize forward- and backward-flat systems.

A dynamic extension enables exact linearization of (x,u)-flat systems.

Framework unifies flatness analysis for two-input discrete-time systems.

Abstract

In this contribution we discuss flat discrete-time nonlinear systems in a general setting including two special subclasses, namely, forward- and backward-flat systems. We relate rank conditions for certain submatrices of the Jacobian of the flat parameterization to the mentioned subclasses. Motivated by these rank conditions, for the case of two-input systems that possess an (x,u)-flat output, we derive a simple type of dynamic extension for the purpose of an exact linearization.