论文标题
$ k $阳性系统的平衡截断
Balanced truncation of $k$-positive systems
论文作者
论文摘要
本文考虑了离散时间Hankel $ k $阳性系统的平衡截断，其特征是Hankel矩阵的未成年人订购$ K $的未成年人。我们的主要结果表明，如果截短系统的订单$ K $或更短，那么Hankel完全正（$ \ infty $ - 阳性），这意味着它是一阶滞后的总和。该结果可以理解为两个已知结果之间的桥梁：正系统的一阶截断为正（$ k = 1 $），而平衡截断的属性则保留了状态空间对称性。它提供了一类广泛的系统，可以保证平衡截断，从而导致内部积极的系统最少。
This paper considers balanced truncation of discrete-time Hankel $k$-positive systems, characterized by Hankel matrices whose minors up to order $k$ are nonnegative. Our main result shows that if the truncated system has order $k$ or less, then it is Hankel totally positive ($\infty$-positive), meaning that it is a sum of first order lags. This result can be understood as a bridge between two known results: the property that the first-order truncation of a positive system is positive ($k=1$), and the property that balanced truncation preserves state-space symmetry. It provides a broad class of systems where balanced truncation is guaranteed to result in a minimal internally positive system.
