Analysis and control of max-plus linear discrete-event systems: An introduction

Bart De Schutter*, Ton van den Boom, Jia Xu, Samira Safaei Farahani

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

15 Citations (Scopus)
108 Downloads (Pure)


The objective of this paper is to provide a concise introduction to the max-plus algebra and to max-plus linear discrete-event systems. We present the basic concepts of the max-plus algebra and explain how it can be used to model a specific class of discrete-event systems with synchronization but no concurrency. Such systems are called max-plus linear discrete-event systems because they can be described by a model that is “linear” in the max-plus algebra. We discuss some key properties of the max-plus algebra and indicate how these properties can be used to analyze the behavior of max-plus linear discrete-event systems. Next, some control approaches for max-plus linear discrete-event systems, including residuation-based control and model predictive control, are presented briefly. Finally, we discuss some extensions of the max-plus algebra and of max-plus linear systems.

Original languageEnglish
Pages (from-to)25-54
JournalDiscrete Event Dynamic Systems: theory and applications
Issue number1
Publication statusPublished - 2020


  • Analysis of discrete-event systems
  • Max-plus algebra
  • Max-plus linear systems
  • Model predictive control
  • Model-based control of max-plus linear systems
  • Residuation-based control
  • Survey


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