From Partial and Horizontal Contraction to k-Contraction

• 成果类型: Article
• 署名作者: Wu, Chengshuai; Dimarogonas, Dimos V.
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3303037
• 发表日期: 2024
• 页码: 2391-2398
• 关键词: Andronov-Hopf oscillator; compound matrix; horizontal contraction; k-contraction; partial contraction; virtual contraction

摘要

A geometric generalization of contraction theory called k-contraction was recently developed using k-compound matrices. In this article, 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.