In this paper, necessary and sufficient conditions for the polyhedron set to be a positively invariant polyhedron of a discrete-time positive linear system subject to external disturbances are established. By solving a set of inequalities, which is also a linear programming, necessary and sufficient conditions for the existence of positive invariant polyhedra for discrete-time positive linear systems are proposed, and the relationship between Lyapunov stability and positively invariant polyhedron is also investigated, numerical examples illustrate our results.

中文翻译：

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离散时间正线性系统的正不变多面体

本文建立了受外部扰动的离散时间正线性系统的多面体集合为正不变多面体的充要条件。通过求解一组不等式（也是线性规划），提出了离散时间正线性系统正不变多面体存在的充要条件，并研究了李亚普诺夫稳定性与正不变多面体之间的关系，数值模拟例子说明了我们的结果。