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

2025/10/31 by Johannes Schrotshamer, Schrotshamer, Johannes, Bernd Kolar +3
Engineering · Mathematics · #Control and Dynamics of Mobile Robots #Advanced Differential Equations and Dynamical Systems #Adaptive Control of Nonlinear Systems

paper · pdf · doi:10.48550/arxiv.2510.27380

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.

Citations

• A Dual Geometric Test for Forward-Flatness
• Dynamic feedback linearization of two-input control systems via successive one-fold prolongations

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• A Flat Triangular Form for Nonlinear Systems with Two Inputs: Necessary\n and Sufficient Conditions
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