TY - JOUR

T1 - Max-plus algebra and system theory

T2 - Where we are and where to go now

AU - Cohen, Guy

AU - Gaubert, Stéphane

AU - Quadrat, Jean Pierre

N1 - Funding Information:
1 This work has been partially supported by a TMR contract No. ERB-FMRX-CT-96-0074 of the European Community in the framework of the ALAPEDES network.

PY - 1999/1/1

Y1 - 1999/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0032632040&partnerID=8YFLogxK

U2 - 10.1016/S1367-5788(99)00023-1

DO - 10.1016/S1367-5788(99)00023-1

M3 - Article

AN - SCOPUS:0032632040

SN - 1367-5788

VL - 23

SP - 207

EP - 219

JO - Annual Reviews in Control

JF - Annual Reviews in Control

ER -