In this overview report we present known results and open problems in connection with the minimal state space realization problem in the max-plus algebra, which is a framework that can be used to model a class of discrete event systems. 1 Description of the problem Given an n×n matrix A, an n×1 vector b and a 1×n vector c one can construct the sequence gi, i = 1, 2, . . ., where gi is defined b...

We show that the problem of finding a singular value decomposition of a matrix in the extended max algebra can be reformulated as an Extended Linear Complementarity Problem. This allows us to compute all the max-algebraic singular value decompositions of a matrix. This technique can also be used to calculate many other max-algebraic matrix decompositions.

asynchronous circuit, clock schedule verification, cycle time, fixed point, max-plus algebra, min-max function Recent progress in the timing analysis of digital circuits has involved the use of maximum and minimum timing constraints. We put forward the theory of min-max functions, a non-linear generalization of max-plus algebra, as the correct framework in which to study problems with mixed con...

We study matrices in the (Max; +) algebra. We introduce a new tool for describing the deterministic spectral behaviour of matrices of size 3 3. It consists in a graphical representation of eigenvectors and domains of attraction in the projective space. It appears to be very helpful in understanding some of the phenomena occurring in this algebra. Une Repr esentation Graphique pour les Matrices ...

An algorithm for solving Min-Goguen fuzzy linear systems of equations is presented in this paper. Solving subject great scientific interest. The authors have developed fast an efficient algorithms over several algebras. Here we present, relatively simple, and to solve algebra, logically backed by previously the max-min min-max