A Method to Find All Solutions of a System of Multivariate Polynomial Equalities and Inequalities in the Max Algebra

Reference

B. De Schutter and B. De Moor, "A Method to Find All Solutions of a System of Multivariate Polynomial Equalities and Inequalities in the Max Algebra," Discrete Event Dynamic Systems: Theory and Applications, vol. 6, no. 2, pp. 115-138, Mar. 1996.

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.

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Bibtex entry

@article{DeSDeM:93-71,
author={B. {D}e Schutter and B. {D}e Moor},
title={A Method to Find All Solutions of a System of Multivariate Polynomial Equalities and Inequalities in the Max Algebra},
journal={Discrete Event Dynamic Systems: Theory and Applications},
volume={6},
number={2},
pages={115--138},
month=mar,
year={1996},
doi={10.1007/BF01797235}
}

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