About difference equations, algebras and discrete events

  • G. J. Olsder
Part of the Mathematics and Its Applications book series (MAIA, volume 81)


An introduction to the theory of discrete event dynamic systems is given. Discrete event dynamic systems (DEDS) are nonlinear in the conventional algebra, but are linear in the max-plus algebra. Of many concepts and results within the conventional linear algebra and linear systems theory duplicates exist in the max-plus algebra and the theory of DEDS. The motivation to study DEDS comes from the description of flows in networks. Such networks are for instance related to computer systems, traffic systems and flexible manufacturing in production planning.


Difference Equation Manufacturing System Transfer Matrix Discrete Event Part Type 
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  1. [1]
    F. Baccelli, G. Cohen, G.J. Olsder, and J.P.Quadrat. Synchronization and Linearity. John Wiley, 1992.zbMATHGoogle Scholar
  2. [2]
    J.G. Braker. Max-algebra modelling and analysis of time-table dependent networks. In Proceedings of the first European Control Conference pages 1831–1836. Hermes, Paris, 1991.Google Scholar
  3. [3]
    R.A. Cuninghame Green. Minimax Algebra . Lecture Notes in Economics and Mathematical Systems, no 166. Springer Verlag, 1979.Google Scholar
  4. [4]
    M. Gondran and M. Minoux. Graphs and Algorithms. John Wiley, 1986.Google Scholar
  5. [5]
    Richard M. Karp. A characterization of the minimum cycle mean in a digraph. Discrete Mathematics 23:309–311, 1978.MathSciNetzbMATHGoogle Scholar
  6. [6]
    Huibert Kwakernaak and Raphael Sivan. Linear Optimal Control Systems. Wiley-Interscience, New York, 1972.zbMATHGoogle Scholar
  7. [7]
    G.J. Olsder and R.E. de Vries. On an analogy of minimal realizations in conventional and discrete-event dynamic systems. In P. Varaiya and A. B. Kurzhanski, editors Discrete Event Systems: Models and Applications volume 103 of Lecture Notes in Control and Information Sciences pages 149–161. Springer Verlag, Berlin, 1988.Google Scholar
  8. [8]
    James L. Peterson. Petri net theory and the modeling of systems .Prentice Hall, Englewood Cliffs, N.J. 07632, 1981.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1992

Authors and Affiliations

  • G. J. Olsder
    • 1
  1. 1.Faculty of Technical Mathematics and InformaticsDelft University of TechnologyDelftThe Netherlands

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