Max-plus algebra is a discrete algebraic system developed on the operations max () and plus src=image/13420822_03.gif>), where are defined as addition multiplication in conventional algebra. This structure semi-ring with its elements being real numbers along ε=-∞ e=0. On other hand, synchronized event problem which an scheduled to meet deadline. There two aspects ...

A direct application of Zorn’s lemma gives that every Lipschitz map f : X ⊂ Qp → Qp has an extension to a Lipschitz map f̃ : Qp → Qp . This is analogous to, but easier than, Kirszbraun’s theorem about the existence of Lipschitz extensions of Lipschitz maps S ⊂ Rn → R`. Recently, Fischer and Aschenbrenner obtained a definable version of Kirszbraun’s theorem. In this paper, we prove in the p-adic ...

The main purpose of this paper is to propose five programs in C for matrix computations and solving recurrent equations systems with entries in max plus algebra. 1

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 ...

Zorn’s lemma is a result in set theory that appears in proofs of some non-constructive existence theorems throughout mathematics. We will state Zorn’s lemma below and use it in later sections to prove some results in linear algebra, ring theory, and group theory. In an appendix, we will give an application to metric spaces. The statement of Zorn’s lemma is not intuitive, and some of the termino...

Let a b = max(a; b) and a b = a + b for a; b 2 R := R [ f 1g. By max-algebra we understand the analogue of linear algebra developed for the pair of operations ( ; ), extended to matrices and vectors. The symbol A stands for the k max-algebraic power of a square matrix A. Let us denote by " the max-algebraic "zero" vector, all the components of which are 1: The max-algebraic eigenvalue-eigenvect...

The max-plus algebra is one of the frameworks that can be used to model discrete event systems. One of the open problems in the max-plus-algebraic system theory for discrete event systems is the minimal realization problem. In this paper we present some results for a simplified version of the general minimal realization problem: the boolean minimal realization problem, i.e., we consider models ...