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 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.

In max-plus algebra, some algorithms for determining the eigenvector of irreducible matrices are power algorithm and Kleene star algorithm. this research, a modified will be discussed to compensate disadvantages The algorithm’s time complexity is O(n(n!)), new O(n4), while cannot calculated. This research also applies algebra in railroad network scheduling problem, constructing graphical user i...

The purpose of this paper is to study the tropical algebra – the algebra over the tropical semi-ring. We start by introducing a third approach to arithmetic over the max-plus semi-ring which generalizes the two other concepts in use. Regarding this new arithmetic, matters of tropical matrices are discussed and the properties of these matrices are studied. These are the preceding phases toward t...

Abstract The basic filters in mathematical morphology are dilation and erosion. They defined by a structuring element that is usually shifted pixel-wise over an image, together with comparison process takes place within the corresponding mask. This made grey value case means of maximum or minimum formation. Hence, there easy access to max-plus algebra and, change, also theory linear algebra. We...

In this paper, stochastic stabilization is investigated by max-plus algebra for a Markovian jump cloud control system with reference signal. For the system, there exists framework adjustment whose evolution satisfied Markov chain. Using algebra, used to describe system. A causal feedback matrix obtained exponential stability analysis controller of sufficient condition given ensure existence on ...

If we consider the real numbers extended by minus infinity with the operations maximum and addition, we obtain the max-algebra or the max-plus semiring. The analog of linear algebra for these operations extended to matrices and vectors has been widely studied. We outline some facts on semirings and max-plus linear algebra, in particular, the solution of maxplus linear systems. As an application...