Reachable set analysis for linear systems with discrete and distributed delays

Zhiqiang Zuo; Daniel W.C. Ho; Yijing Wang

doi:10.1109/WCICA.2010.5554392

Reachable set analysis for linear systems with discrete and distributed delays

Zhiqiang Zuo
, Daniel W.C. Ho
, Yijing Wang

Department of Mathematics

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

Abstract

This paper is concerned with the reachable set analysis for linear systems with both discrete and distributed delays. By choosing appropriate Lyapunov-Krasovkii functionals, some sufficient conditions are established to ensure that all the states starting from the origin are bounded by an ellipsoid. It is shown that finding the smallest possible ellipsoid can be transformed into an optimization problem with matrix inequality constraints. In addition, the computational complexity is greatly reduced since much fewer variables are involved in the obtained results. These criteria are also extended to systems subject to polytopic uncertainties. It is shown that, in the absence of distributed delay, the obtained condition is less conservative than the existing ones. © 2010 IEEE.

Original language	English
Title of host publication	Proceedings of the World Congress on Intelligent Control and Automation (WCICA)
Pages	2085-2090
DOIs	https://doi.org/10.1109/WCICA.2010.5554392
Publication status	Published - 2010
Event	2010 8th World Congress on Intelligent Control and Automation, WCICA 2010 - Jinan, China Duration: 7 Jul 2010 → 9 Jul 2010

Conference

Conference	2010 8th World Congress on Intelligent Control and Automation, WCICA 2010
Place	China
City	Jinan
Period	7/07/10 → 9/07/10

Research Keywords

Matrix inequality
Polytopic uncertainties
Reachable set bounding
Time delay systems

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10.1109/WCICA.2010.5554392

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@inproceedings{e0e6811eac064b939b1a6e175806766f,

title = "Reachable set analysis for linear systems with discrete and distributed delays",

abstract = "This paper is concerned with the reachable set analysis for linear systems with both discrete and distributed delays. By choosing appropriate Lyapunov-Krasovkii functionals, some sufficient conditions are established to ensure that all the states starting from the origin are bounded by an ellipsoid. It is shown that finding the smallest possible ellipsoid can be transformed into an optimization problem with matrix inequality constraints. In addition, the computational complexity is greatly reduced since much fewer variables are involved in the obtained results. These criteria are also extended to systems subject to polytopic uncertainties. It is shown that, in the absence of distributed delay, the obtained condition is less conservative than the existing ones. {\textcopyright} 2010 IEEE.",

keywords = "Matrix inequality, Polytopic uncertainties, Reachable set bounding, Time delay systems",

author = "Zhiqiang Zuo and Ho, \{Daniel W.C.\} and Yijing Wang",

year = "2010",

doi = "10.1109/WCICA.2010.5554392",

language = "English",

isbn = "9781424467129",

pages = "2085--2090",

booktitle = "Proceedings of the World Congress on Intelligent Control and Automation (WCICA)",

note = "2010 8th World Congress on Intelligent Control and Automation, WCICA 2010 ; Conference date: 07-07-2010 Through 09-07-2010",

}

Reachable set analysis for linear systems with discrete and distributed delays. / Zuo, Zhiqiang; Ho, Daniel W.C.; Wang, Yijing.
Proceedings of the World Congress on Intelligent Control and Automation (WCICA). 2010. p. 2085-2090 5554392.

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

TY - GEN

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AU - Zuo, Zhiqiang

AU - Ho, Daniel W.C.

AU - Wang, Yijing

PY - 2010

Y1 - 2010

N2 - This paper is concerned with the reachable set analysis for linear systems with both discrete and distributed delays. By choosing appropriate Lyapunov-Krasovkii functionals, some sufficient conditions are established to ensure that all the states starting from the origin are bounded by an ellipsoid. It is shown that finding the smallest possible ellipsoid can be transformed into an optimization problem with matrix inequality constraints. In addition, the computational complexity is greatly reduced since much fewer variables are involved in the obtained results. These criteria are also extended to systems subject to polytopic uncertainties. It is shown that, in the absence of distributed delay, the obtained condition is less conservative than the existing ones. © 2010 IEEE.

AB - This paper is concerned with the reachable set analysis for linear systems with both discrete and distributed delays. By choosing appropriate Lyapunov-Krasovkii functionals, some sufficient conditions are established to ensure that all the states starting from the origin are bounded by an ellipsoid. It is shown that finding the smallest possible ellipsoid can be transformed into an optimization problem with matrix inequality constraints. In addition, the computational complexity is greatly reduced since much fewer variables are involved in the obtained results. These criteria are also extended to systems subject to polytopic uncertainties. It is shown that, in the absence of distributed delay, the obtained condition is less conservative than the existing ones. © 2010 IEEE.

KW - Matrix inequality

KW - Polytopic uncertainties

KW - Reachable set bounding

KW - Time delay systems

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DO - 10.1109/WCICA.2010.5554392

M3 - RGC 32 - Refereed conference paper (with host publication)

SN - 9781424467129

SP - 2085

EP - 2090

BT - Proceedings of the World Congress on Intelligent Control and Automation (WCICA)

T2 - 2010 8th World Congress on Intelligent Control and Automation, WCICA 2010

Y2 - 7 July 2010 through 9 July 2010

ER -

Reachable set analysis for linear systems with discrete and distributed delays

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