In this paper we introduce and study weakly linear systems, i.e. systems consisting of matrix inequalities Eqs. 17–20, over the max-plus quantale which is also known as complete max-plus algebra. We prove the existence of the greatest solution contained in a given matrix X₀, and present a procedure for its computation. In the case of weakly linear systems consisting of finitely many matrix inequalities, when all finite elements of matrices X₀, A_s and B_s, s ∈ I are integers, rationals or particular irrationals and a finite solution exists, the procedure finishes in a finite number of steps. If in that case an arbitrary finite solution is given, a lower bound on the number of computational steps is calculated. Otherwise, we use our algorithm to compute approximations to finite solutions.

在本文中，我们介绍并研究弱线性系统，即由矩阵不等式组成的系统。 17-20，关于 max-plus Quantale，也称为完全 max-plus 代数。我们证明了给定矩阵X ₀中包含的最大解的存在性，并给出了其计算过程。对于由有限多个矩阵不等式组成的弱线性系统，当矩阵X ₀、A _s和B _s、s ∈ I的所有有限元都是整数、有理数或特定无理数且存在有限解时，该过程以有限数量的步骤。如果在这种情况下给出任意有限解，则计算计算步骤数的下限。否则，我们使用我们的算法来计算有限解的近似值。