Comparison and aggregation of max-plus linear systems (Q1826727)

The authors study finite dynamical systems which are not linear, but are linear with respect to the max-plus algebra \(R_{\max}\), which has as underlying set the real numbers together with \(\{-\infty\}\), but the addition and multiplication operations \(\oplus\) and \(\otimes\) are defined by \[ x\oplus y=\max\{x,y\},\;\;\;x\otimes y=x+y. \] A new preorder is defined, and explicit methods are developed to find bounds on the state vectors of a lumped system.