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Discrete Event Dynamic Systems

, Volume 6, Issue 2, pp 115–138 | Cite as

A method to find all solutions of a system of multivariate polynomial equalities and inequalities in the max algebra

  • Bart de Schutter
  • Bart de Moor
Article

Abstract

In this paper we show that finding solutions of a system of multivariate polynomial equalities and inequalities in the max algebra is equivalent to solving an Extended Linear Complementarity Problem. This allows us to find all solutions of such a system of multivariate polynomial equalities and inequalities and provides a geometrical insight in the structure of the solution set. We also demonstrate that this enables us to solve many important problems in the max algebra and the max-min-plus algebra such as matrix decompositions, construction of matrices with a given characteristic polynomial, state space transformations and the (minimal) state space realization problem.

Keywords

max algebra multivariate max-algebraic polynomial equalities and inequalities state space models extended linear complementarity problem 

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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Bart de Schutter
    • 1
  • Bart de Moor
    • 1
  1. 1.ESAT/SISTAKatholieke Universiteit LeuvenLeuvenBelgium

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