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Comparison and aggregation of max-plus linear systems. (English) Zbl 1052.15014
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.

15A45 Miscellaneous inequalities involving matrices
93C65 Discrete event control/observation systems
16Y60 Semirings
15A30 Algebraic systems of matrices
Full Text: DOI Link
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