From Partial and Horizontal Contraction to <italic>K</italic>-Contraction

Chengshuai Wu; Dimos V. Dimarogonas

doi:10.1109/TAC.2023.3303037

From Partial and Horizontal Contraction to <italic>K</italic>-Contraction

Chengshuai Wu, Dimos V. Dimarogonas

Research output: Contribution to journal › Article › peer-review

Abstract

A geometric generalization of contraction theory called <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-contraction was recently developed using <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-compound matrices. In this note, we focus on the relations between <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-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 <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-contraction. We use the Andronov-Hopf oscillator to demonstrate some of the theoretical results.

Original language	English
Pages (from-to)	1-8
Number of pages	8
Journal	IEEE Transactions on Automatic Control
DOIs	https://doi.org/10.1109/TAC.2023.3303037
State	Accepted/In press - 2023
Externally published	Yes

Keywords

<inline-formula xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"> <tex-math notation="LaTeX">$k$</tex-math> </inline-formula>-contraction
Andronov-Hopf oscillator
Behavioral sciences
compound matrix
Compounds
horizontal contraction
Manifolds
Oscillators
partial contraction
Sufficient conditions
Synchronization
Trajectory
virtual contraction

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10.1109/TAC.2023.3303037

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title = "From Partial and Horizontal Contraction to K-Contraction",

abstract = "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.",

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author = "Chengshuai Wu and Dimarogonas, {Dimos V.}",

note = "Publisher Copyright: IEEE",

year = "2023",

doi = "10.1109/TAC.2023.3303037",

language = "אנגלית",

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journal = "IEEE Transactions on Automatic Control",

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AU - Wu, Chengshuai

AU - Dimarogonas, Dimos V.

N1 - Publisher Copyright: IEEE

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

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KW - Behavioral sciences

KW - compound matrix

KW - Compounds

KW - horizontal contraction

KW - Manifolds

KW - Oscillators

KW - partial contraction

KW - Sufficient conditions

KW - Synchronization

KW - Trajectory

KW - virtual contraction

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SN - 0018-9286

SP - 1

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JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

ER -

From Partial and Horizontal Contraction to <italic>K</italic>-Contraction

Abstract

Keywords

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