Max-plus algebra and system theory: Where we are and where to go now

Guy Cohen, Stéphane Gaubert, Jean Pierre Quadrat

Research output: Contribution to journalArticlepeer-review

148 Scopus citations


More than sixteen years after the beginning of a linear theory for certain discrete event systems in which max-plus algebra and similar algebraic tools play a central role, this paper attempts to summarize some of the main achievements in an informal style based on examples. By comparison with classical linear system theory, there are areas which are practically untouched, mostly because the corresponding mathematical tools are yet to be fabricated. This is the case of the geometric approach of systems which is known, in the classical theory, to provide another important insight to system-theoretic and control-synthesis problems, beside the algebraic machinery. A preliminary discussion of geometric aspects in the max-plus algebra and their use for system theory is proposed in the last part of the paper.

Original languageEnglish
Pages (from-to)207-219
Number of pages13
JournalAnnual Reviews in Control
StatePublished - 1 Jan 1999
Externally publishedYes

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering


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