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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.

##### MSC:
 15A45 Miscellaneous inequalities involving matrices 93C65 Discrete event control/observation systems 16Y60 Semirings 15A30 Algebraic systems of matrices
UMDES
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##### References:
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