论文标题
从部分和水平收缩到$ k $ - 收集
From Partial and Horizontal Contraction to $k$-Contraction
论文作者
论文摘要
最近使用$ k $ compound矩阵开发了一种称为〜$ k $ contraction的收缩理论的几何概括。在本说明中，我们专注于$ K $ contraction和其他两个广义收缩框架之间的关系：部分收缩（也称为虚拟收缩）和水平收缩。我们表明，这三个收缩概念通常是不同的。我们在这里提供了新的足够条件，以确保部分收缩意味着水平收缩，并且水平收缩意味着$ k $ - 征收。我们使用Andronov-HOPF振荡器来证明一些理论结果。
A geometric generalization of contraction theory called~$k$-contraction was recently developed using $k$-compound matrices. In this note, we focus on the relations between $k$-contraction and two other generalized contraction frameworks: partial contraction (also known as virtual contraction) and horizontal contraction. We show that in general these three notions of contraction are different. We here provide new sufficient conditions guaranteeing that partial contraction implies horizontal contraction, and that horizontal contraction implies $k$-contraction. We use the Andronov-Hopf oscillator to demonstrate some of the theoretical results.
