@INPROCEEDINGS{maxplus90b, author={Max Plus}, title={Linear systems in (max,+)-algebra}, booktitle={Proceedings of the 29th Conference on Decision and Control}, year={1990}, address={Honolulu}, month={Dec.}, }

Max Plus is a collective name for a working group on Discrete Event Systems Theory, at INRIA (META2 Project) composed (at the time of the paper) of Marianne Akian, Guy Cohen, Stéphane Gaubert, Ramine Nikoukhah, and Jean Pierre Quadrat.

In this paper, we study the general system of linear equations in the (max,+) algebra. We introduce a symmetrization of this algebra and a new notion called balance which generalizes classical equations. This construction results in the linear closure of the (max,+) algebra in the sense that every non-degenerate system of linear balances has a unique solution given by Cramer's rule.