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.