**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.

Online version of the paper

Corresponding technical report: pdf file (253 KB)

@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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