From Partial and Horizontal Contraction to [Formula Omitted]-Contraction

A geometric generalization of contraction theory called [Formula Omitted]-contraction was recently developed using [Formula Omitted]-compound matrices. In this article, we focus on the relations between [Formula Omitted]-contraction and two other generalized contraction frameworks: partial contracti...

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Bibliographic Details
Published inIEEE transactions on automatic control Vol. 69; no. 4; p. 2391
Main Authors Wu, Chengshuai, Dimarogonas, Dimos V
Format Journal Article
LanguageEnglish
Published New York The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 01.01.2024
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Summary:A geometric generalization of contraction theory called [Formula Omitted]-contraction was recently developed using [Formula Omitted]-compound matrices. In this article, we focus on the relations between [Formula Omitted]-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 [Formula Omitted]-contraction. We use the Andronov–Hopf oscillator to demonstrate some of the theoretical results.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2023.3303037