AN OVERVIEW OF MAX-PLUS LINEAR SYSTEMS

• Journal title : Honam Mathematical Journal
• Volume 33, Issue 1,  2011, pp.93-113
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2011.33.1.093
Title & Authors
AN OVERVIEW OF MAX-PLUS LINEAR SYSTEMS
Kim, Yong-Gu; Shin, Hyun-Hee;

Abstract
Let $\small{a{\oplus}b}$ = max(a, b), $\small{a{\otimes}b}$=a+b, a, $\small{b\in\mathbb{R}_{\varepsilon}\;:=\cup\{-\infty\}}$. In max-plus algebra we work on the linear algebra structure for the pair of operations ($\small{{\oplus},{\otimes}}$) extended to matrices and vectors over $\small{\mathbb{R}_{\varepsilon}}$. In this paper our main aim is to reproduce the work of R. A. Cuninghame-Green [3] on the linear systems over a max-plus semi-field $\small{\mathbb{R}_{\varepsilon}}$.
Keywords
Max-plus algebra;Linear equations;Tropical Geometry;
Language
English
Cited by
References
1.
F.L. Baccelli, G. Cohen, G.-J. Olsder, J.-P. Quadrat, Synchronization and Linearity, John Wiley, Chichester, New York, 1992.

2.
P. Butkovic, Max-algebra: the linear algebra of combinatorics? Linear Algebra Appl. bf 367 (2003), 313-335.

3.
R. Cuninghame-Green, Minimax-Algebra, Lecture Notes in Economics and Math. Systems, Vol. 166, Springer-Verlag, New York, Heidelberg, Berlin 1979.

4.
B. De Schutter, Max-Algebraic system theory for discrete event systems, Katholiceke Universiteit Press, 1994.

5.
D. Speyer, B. Sturmfels, Tropical Matematics, Preprint arXiv:math.Co/04080099.