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
@article{DeSDeM:93-71,
author = {De Schutter, Bart and De Moor, Bart},
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}
}