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The characteristic equation and minimal state space realization of SISO systems in the max algebra

  • Bart De Schutter
  • Bart De Moor
The Max-Plus Algebraic Approach
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 199)

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References

  1. 1.
    F. Baccelli, G. Cohen, G.J. Olsder, and J.P. Quadrat, Synchronization and Linearity. New York: John Wiley & Sons, 1992.Google Scholar
  2. 2.
    R.A. Cuninghame-Green, “Algebraic realization of discrete dynamic systems,” in Proceedings of the 1991 IFAC Workshop on Discrete Event System Theory and Applications in Manufacturing and Social Phenomena, Shenyang, China, pp. 11–15, June 1991.Google Scholar
  3. 3.
    B. De Schutter and B. De Moor, “Minimal state space realization of SISO systems in the max algebra,” Technical Report 93-57, ESAT/SISTA, Katholieke Universiteit Leuven, Kardinaal Mercierlaan 94, B-3001 Leuven, Belgium, 1993.Google Scholar
  4. 4.
    B. De Schutter and B. De Moor, “Minimal realization in the max algebra is an extended linear complementarity problem,” Technical Report 93-70A, ESAT/SISTA, Katholieke Universiteit Leuven, Kardinaal Mercierlaan 94, B-3001 Leuven, Belgium, 1993. Submitted to Systems & Control Letters.Google Scholar
  5. 5.
    B. De Schutter and B. De Moor, “A method to find all solutions of a set of multivariate polynomial equalities and inequalities in the max algebra,” Technical Report 93-71, ESAT/SISTA, Katholieke Universiteit Leuven, Kardinaal Mercierlaan 94, B-3001 Leuven, Belgium, 1993. Submitted to Discrete Event Dynamic Systems: Theory and Applications.Google Scholar
  6. 6.
    S. Gaubert, Théorie des Systèmes Linéaires dans les Dioïdes. PhD thesis, Ecole Nationale Supérieure des Mines de Paris, France, July 1992.Google 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 Proceedings of the CNRS/CNET/INRIA Seminar, Algèbres Exotiques et Systèmes à Evénements Discrets, INRIA, Rocquencourt, France, June 1987.Google Scholar
  8. 8.
    L. Wang and X. Xu, “On minimal realization of SISO DEDS over max algebra,” in Proceedings of the 2nd European Control Conference, Groningen, The Netherlands, pp. 535–540, June 1993.Google Scholar

Copyright information

© Springer-Verlag London Limited 1994

Authors and Affiliations

  • Bart De Schutter
    • 1
  • Bart De Moor
    • 1
  1. 1.ESAT-Katholieke Universiteit LeuvenLeuvenBelgium

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