This paper deals with the modeling of the time behavior of discrete-event systems in (max, +) algebra. The systems we consider are linearly modeled in this algebra. The proposed method is inspired by conventional linear system theory : from an ARMA form of the model and the system impulse response, the model parameters are computed by using a basic result of Residuation Theory in order to minim...

The topics of this paper are matrix factorizations and the minimal state space realization problem in the maxplus algebra, which is one of the modeling frameworks that can be used to model discrete event systems. We present a heuristic algorithm to compute a factorization of a matrix in the max-plus algebra. Next we use this algorithm to determine the minimal system order (and to construct a mi...

Abstract: Discrete event systems involving synchronization and delay phenomena can be described by a linear state representation over (max,+) algebra. Some discrete event systems involving choice phenomena could be transformed, under some conditions, into switching max-plus linear systems modeled as automata. The switching between states of these automata is governed by a switching variable. Th...

The topic of this paper is the (partial) minimal realization problem in the max algebra, which is one of the modeling frameworks that can be used to model discrete event systems. We use the fact that a system of multivariate max-algebraic polynomial equalities can be transformed into an Extended Linear Complementarity Problem to find all equivalent minimal state space realizations of a multiple...

The topic of this paper is the (partial) minimal realization problem in the max algebra, which is one of the modeling frameworks that can be used to model discrete event systems. We use the fact that a system of multi-variate max-algebraic polynomial equalities can be transformed into an Extended Linear Complementarity Problem to nd all equivalent minimal state space realizations of a multiple ...

In this paper, the concept of complete finite prefixes for process algebra expressions is extended to stochastic models. Events are supposed to happen after a delay that is determined by random variables assigned to the preceding conditions. Max-plus algebra expressions are shown to provide an elegant notation for stochastic prefixes not containing any decisions. Furthermore, they allow for the...

Duality between the coloured quantum group and the coloured quantum algebra corresponding to GL(2) is established. The coloured L functionals are constructed and the dual algebra is derived explicitly. These functionals are then employed to give a coloured generalisation of the differential calculus on quantum GL(2) within the framework of the R-matrix approach. Lett. Math. Phys. 53 (2000) 29-4...

The topics of this paper are state space transformations and the (partial) state space problem in the max algebra, which is one of the modeling frameworks that can be used to model discrete event systems. We use the fact that a system of multivariate max-algebraic polynomial equations can be transformed into an Extended Linear Complementarity Problem to perform state space transformations and t...

The dater equalities constitutes an appropriate tool which allows a linear description of Timed Event Graphs in the field of (max, +) algebra. This paper proposes an equivalent model in the usual algebra which can describe Timed and P-time Event Graphs. Considering 1-periodic behavior, the application of a variant of Farkas’ lemma allows the determination of upper and lower bounds of the produc...

We consider the recursive equation \x(n + 1) = A(n) x(n)" where x(n + 1) and x(n) are R k-valued vectors and A(n) is an irreducible random matrix of size k k. The matrix-vector multiplication in the (max,+) algebra is deened by (A(n) x(n)) i = max j (A ij (n) + x j (n)). This type of equation can be used to represent the evolution of Stochastic Event Graphs which include cyclic Jackson Networks...