@INPROCEEDINGS{maxplus91a, author={Max Plus}, title={A linear system theory for systems subject to synchronization and saturation constraints}, booktitle={Proceedings of the first European Control Conference}, year={1991}, address={Grenoble}, month={July}, }

A linear system theory is developed for a class of continuous and discrete Systems subject to Synchronization and Saturations that we call $S^3$. This class provides a generalization of a particular class of timed discrete event systems which can be modeled as event graphs. The development is based on a linear modeling of $S^3$ in the min-plus algebra. This allows us to extend elementary notions and a number of results of conventional systems to $S^3$. In particular, notions of causality, time-invariance, impulse response, convolution, transfer function and rationality are considered.