A graph-oriented approach to address generically flat outputs in structured LTI discrete-time systems

Journal article (2022)

Authors

Taha Boukhobza Lorraine University
J.W. van der Woude Mathematical Physics - EEMCS
Christian Commault Université Grenoble Alpes
Gilles Millérioux Lorraine University
Research Group
Mathematical Physics (EEMCS) (TU Delft)
Copyright: © 2022 Taha Boukhobza, J.W. van der Woude, Christian Commault, Gilles Millérioux
DOI: https://doi.org/10.1016/j.automatica.2022.110344
Graph theory Flatness Structured linear systems
More Info
expand_more

Published Date

2022

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Mathematical Physics

Abstract

This paper addresses difference flatness for structured LTI discrete-time systems. Two forms of necessary and sufficient conditions for an output to be a structural flat output are given. First, a preliminary result algebraically defines a flat output in terms of invariant zeros regardless whether an LTI system is structured or not. Next, the conditions are expressed in terms of graphical conditions to define a structural flat output. Checking for the graphical conditions calls for algorithms that have polynomial-time complexity and that are commonly used for digraphs. The tractability of the conditions is illustrated on several examples.