Based on max-plus algebra, a class of discrete event processes can be described by linear recursive equations[1]. Such a system exhibits asymptotic periodic behavior, and its performance can be evaluated by calculating the eigenvalue of the system matrix in max-plus algebra. On the other hand, control techniques based on switching among different controllers have been explored extensively in re...

This paper summarizes results on some topics in the max-plus convex geometry, mainly concerning the role of multiorder, Kleene stars and cyclic projectors, and relates them to some topics in max algebra. The multiorder principle leads to max-plus analogues of some statements in the finite-dimensional convex geometry and is related to the set covering conditions in max algebra. Kleene stars are ...

We describe the specialization to max-plus algebra of Howard’s policy improvement scheme, which yields an algorithm to compute the solutions of spectral problems in the max-plus semiring. Experimentally, the algorithm shows a remarkable (almost linear) average execution time. Résumé: Nous spécialisons à l’algèbre max-plus l’itération sur les politiques de Howard, qui fournit un algorithme pour ...

We present necessary and sufficient criteria for a max-algebraic supereigenvector, i.e., solution of the system $A\otimes\textbf{x}\geq\textbf{x}$ with $A\in\overline{\mathbb{R}}^{n\times n}$ in max-plus algebra, to be an extremal. also show that suggested extremality can verified $O(n^2)$ time any given $\textbf{x}$.

We present an extended version of max-plus algebra which includes the inverse operator of “max”. This algebra enables us to ultra-discretize the system including subtractions and obtain new ultra-discrete equations. The known ultra-discrete equations can also be recovered by this construction. PACS numbers: 02.30.Ik, 02.30.Jr, 05.45.Yv