Exponential synchronization of partial-state coupled linear systems via contraction analysis

Qichao Ma; Ku Du; Yu Kang; Wei Xing Zheng; Jiahu Qin

doi:10.1109/IECON.2016.7793665

Exponential synchronization of partial-state coupled linear systems via contraction analysis

Qichao Ma, Ku Du, Yu Kang, Wei Xing Zheng, Jiahu Qin

Western Sydney University

Research output: Chapter in Book / Conference Paper › Conference Paper › peer-review

Abstract

In this paper, the contraction theory is used to analyze the synchronization for a collection of partial-state linearly coupled linear systems. First, the synchronization problem of the linear systems is transformed by defining proper error variables such that a stability problem of error systems is to be investigated. Then, the contraction analysis is performed with respect to the error system dynamics. It turns out that the error system dynamics is contracting, which in turn proves that the original systems reach synchronization exponentially fast. In addition, a brief comparison between Lyapunov method and contraction analysis is also provided. Finally, two examples are presented in order to illustrate the effectiveness of the theoretical result.

Original language	English
Title of host publication	Proceedings of the IECON 2016: 42nd Annual Conference of the IEEE Industrial Electronics Society, 24-27 October 2016, Florence, Italy
Publisher	IEEE
Pages	5432-5436
Number of pages	5
ISBN (Print)	9781509034741
DOIs	https://doi.org/10.1109/IECON.2016.7793665
Publication status	Published - 2016
Event	IEEE Industrial Electronics Society. Conference - Duration: 24 Oct 2016 → …

Conference

Conference	IEEE Industrial Electronics Society. Conference
Period	24/10/16 → …

Keywords

Lyapunov functions
convergence
coupled mode theory
linear systems
synchronization

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10.1109/IECON.2016.7793665

Cite this

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title = "Exponential synchronization of partial-state coupled linear systems via contraction analysis",

abstract = "In this paper, the contraction theory is used to analyze the synchronization for a collection of partial-state linearly coupled linear systems. First, the synchronization problem of the linear systems is transformed by defining proper error variables such that a stability problem of error systems is to be investigated. Then, the contraction analysis is performed with respect to the error system dynamics. It turns out that the error system dynamics is contracting, which in turn proves that the original systems reach synchronization exponentially fast. In addition, a brief comparison between Lyapunov method and contraction analysis is also provided. Finally, two examples are presented in order to illustrate the effectiveness of the theoretical result.",

keywords = "Lyapunov functions, convergence, coupled mode theory, linear systems, synchronization",

author = "Qichao Ma and Ku Du and Yu Kang and Zheng, {Wei Xing} and Jiahu Qin",

year = "2016",

doi = "10.1109/IECON.2016.7793665",

language = "English",

isbn = "9781509034741",

pages = "5432--5436",

booktitle = "Proceedings of the IECON 2016: 42nd Annual Conference of the IEEE Industrial Electronics Society, 24-27 October 2016, Florence, Italy",

publisher = "IEEE",

note = "IEEE Industrial Electronics Society. Conference ; Conference date: 24-10-2016",

}

Ma, Q, Du, K, Kang, Y, Zheng, WX & Qin, J 2016, Exponential synchronization of partial-state coupled linear systems via contraction analysis. in Proceedings of the IECON 2016: 42nd Annual Conference of the IEEE Industrial Electronics Society, 24-27 October 2016, Florence, Italy. IEEE, pp. 5432-5436, IEEE Industrial Electronics Society. Conference, 24/10/16. https://doi.org/10.1109/IECON.2016.7793665

Exponential synchronization of partial-state coupled linear systems via contraction analysis. / Ma, Qichao; Du, Ku; Kang, Yu et al.
Proceedings of the IECON 2016: 42nd Annual Conference of the IEEE Industrial Electronics Society, 24-27 October 2016, Florence, Italy. IEEE, 2016. p. 5432-5436.

Research output: Chapter in Book / Conference Paper › Conference Paper › peer-review

TY - GEN

T1 - Exponential synchronization of partial-state coupled linear systems via contraction analysis

AU - Ma, Qichao

AU - Du, Ku

AU - Kang, Yu

AU - Zheng, Wei Xing

AU - Qin, Jiahu

PY - 2016

Y1 - 2016

N2 - In this paper, the contraction theory is used to analyze the synchronization for a collection of partial-state linearly coupled linear systems. First, the synchronization problem of the linear systems is transformed by defining proper error variables such that a stability problem of error systems is to be investigated. Then, the contraction analysis is performed with respect to the error system dynamics. It turns out that the error system dynamics is contracting, which in turn proves that the original systems reach synchronization exponentially fast. In addition, a brief comparison between Lyapunov method and contraction analysis is also provided. Finally, two examples are presented in order to illustrate the effectiveness of the theoretical result.

AB - In this paper, the contraction theory is used to analyze the synchronization for a collection of partial-state linearly coupled linear systems. First, the synchronization problem of the linear systems is transformed by defining proper error variables such that a stability problem of error systems is to be investigated. Then, the contraction analysis is performed with respect to the error system dynamics. It turns out that the error system dynamics is contracting, which in turn proves that the original systems reach synchronization exponentially fast. In addition, a brief comparison between Lyapunov method and contraction analysis is also provided. Finally, two examples are presented in order to illustrate the effectiveness of the theoretical result.

KW - Lyapunov functions

KW - convergence

KW - coupled mode theory

KW - linear systems

KW - synchronization

UR - http://handle.westernsydney.edu.au:8081/1959.7/uws:40155

U2 - 10.1109/IECON.2016.7793665

DO - 10.1109/IECON.2016.7793665

M3 - Conference Paper

SN - 9781509034741

SP - 5432

EP - 5436

BT - Proceedings of the IECON 2016: 42nd Annual Conference of the IEEE Industrial Electronics Society, 24-27 October 2016, Florence, Italy

PB - IEEE

T2 - IEEE Industrial Electronics Society. Conference

Y2 - 24 October 2016

ER -

Exponential synchronization of partial-state coupled linear systems via contraction analysis

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Keywords

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