This paper is concerned with the determination of positively invariant polyhedron for positive linear systems subject to external disturbances whose (∞, 1)-norm or (∞, ∞)-norm are bounded by a prescribed constant. Necessary and sufficient conditions for the existence of a positively invariant polyhedron are derived in terms of a set of inequalities which can be solved by linear programming, and the link between Lyapunov stability and positively invariant polyhedron is also revealed.

中文翻译：

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关于连续时间正线性系统的正不变多面体

本文涉及确定正线性系统的正不变多面体的确定，该正线性系统受到外部干扰，其（∞，1）范数或（∞，∞）范数受规定常数限制。根据一组不等式，可以通过线性规划求解，得出存在正不变多面体的充要条件，并且还揭示了李雅普诺夫稳定性与正不变多面体之间的联系。