The generators of the solution space for a system of inequalities

The generators of the solution space for a system of inequalities A⊗x≥xA⊗x≥x are considered in this paper, where A   is a square matrix over R¯=R∪{−∞}, x is a column vector and ⊗ is a max-plus composition. This paper presents some properties of solutions to the system of inequalities and proposes an algorithm to find a set of generators for the solution space of the system of inequalities with A∈R¯n×n.