The purpose of this paper is to investigate the interplay arising between max algebra, convexity and scaling problems. The latter, which have been studied in nonnegative matrix theory, are strongly related to max algebra. One problem is that of strict visualization scaling, defined as, for a given nonnegative matrix A, a diagonal matrix X such that all elements of XAX are less than or equal to ...

The purpose of this paper is to investigate the interplay arising between max algebra, convexity and scaling problems. The latter, which have been studied in nonnegative matrix theory, are strongly related to max algebra. One problem is strict visualisation scaling, which means finding, for a given nonnegative matrix A, a diagonal matrix X such that all elements of XAX are less than or equal to...

If you want to cite this report, please use the following reference instead: B. De Schutter and B. De Moor, " On the sequence of consecutive powers of a matrix in a Boolean algebra, " SIAM Abstract. In this paper we consider the sequence of consecutive powers of a matrix in a Boolean algebra. We characterize the ultimate behavior of this sequence, we study the transient part of the sequence and...

The purpose of this paper is to investigate the interplay arising between max algebra, convexity and scaling problems. The latter, which have been studied in nonnegative matrix theory, are strongly related to max algebra. One problem is that of strict visualization scaling, defined as, for a given nonnegative matrix A, a diagonal matrix X such that all elements of X −1 AX are less than or equal...

In this paper we study the convergence of the max-consensus protocol. Tropical algebra is used to formulate the problem. Necessary and sufficient conditions for convergence of the max-consensus protocol over fixed as well as switching topology networks are given.

The theory of linear systems in the max-plus algebra is developed for the analysis of discrete event systems. The timed event graphs are one of the tools used for modelling these systems, and their behaviour can be described by (max, plus )-linear equations. This paper proposes a control structure for a public transport system. We mainly based the research of this control on the Residuation the...

We show that certain resource optimization problems relative to Timed Event Graphs reduce to linear programs. The auxiliary variables which allow this reduction can be interpreted in terms of eigenvectors in the (min,+) algebra. Keywords—Resource Optimization, Timed Event Graphs, (max,+) algebra, spectral theory.

The max-plus algebra is one of the frameworks that can be used to model discrete event systems. We show that many fundamental problems in the maxplus algebra can be reformulated as a mathematical programming problem: the Extended Linear Complementarity Problem.

A square array whose all rows and columns are different permutations of the same length over symbol set is known as a Latin square. may or not be symmetric. For classification enumeration purposes, symmetric, non-symmetric, conjugate totally symmetric squares play vital roles. This article discusses Eigenproblem non-symmetric in well max-plus algebra. By defining certain vector corresponding to...