论文标题
变化减少线性时间流体系统
Variation diminishing linear time-invariant systems
论文作者
论文摘要
本文研究了$ k $阳性线性时间流动（LTI）系统的变化降低属性，该系统以$ k-1 $符号更改输出的输出最多具有相同变化的输出。我们为有限维系统的Toeplitz和Hankel操作员表征了此属性。我们的主要结果是，这些操作员以$ k $一阶正阳性系统的串联或并行互连形式具有主导近似。通过表达LTI系统的$ K $ - 积极性为$ K $复合LTI系统的外部积极性（即$ 1 $ - 阳性）。我们的表征概括了外部积极系统（$ k = 1 $）和完全正面系统（$ k = \ infty $;也称为放松系统）的众所周知的特性。
This paper studies the variation diminishing property of $k$-positive linear time-invariant (LTI) systems, which map inputs with $k-1$ sign changes to outputs with at most the same variation. We characterize this property for the Toeplitz and Hankel operators of finite-dimensional systems. Our main result is that these operators have a dominant approximation in the form of series or parallel interconnections of $k$ first order positive systems. This is shown by expressing the $k$-positivity of a LTI system as the external positivity (that is, $1$-positivity) of $k$ compound LTI systems. Our characterization generalizes well known properties of externally positive systems ($k=1$) and totally positive systems ($k=\infty$; also known as relaxation systems).
