On Delay-Range-Dependent and Delay-Rate-Dependent Stability for Delayed Systems

Yuan He; Jintian Hu; Shuxia Wang; Liansheng Zhang

doi:doi:10.11648/j.cse.20190302.11

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On Delay-Range-Dependent and Delay-Rate-Dependent Stability for Delayed Systems

Yuan He, Jintian Hu, Shuxia Wang, Liansheng Zhang

Published in Control Science and Engineering (Volume 3, Issue 2)

Received: 27 September 2019 Accepted: 22 October 2019 Published: 28 October 2019

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Abstract

It is well known that the phenomena of time delays are frequently encountered in many process and various control systems. The presence of delays can have an effect on system stability and performance, so ignoring them may lead to design flaws and incorrect analysis conclusions. Hence, the stability problem for time-delayed systems has received considerable attention in recent years. This brief focuses on the stability analysis for a class of delayed linear systems. Firstly, we construct a novel augmented Lyapunov-Krasovskii functional (LKF) which includes the lower, the upper bounds of the delay and the delay itself. Secondly, utilizing some integral inequalities and the reciprocally convex combination lemma, we obtain less conservative stability criteria formulated in form of linear matrix inequalities (LMIs). Finally, numerical examples are provided to show the effectiveness of the proposed method.

Published in	Control Science and Engineering (Volume 3, Issue 2)
DOI	10.11648/j.cse.20190302.11
Page(s)	20-28
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Time Delay, Lyapunov-Krasovskii Functional (LKF), Linear Matrix Inequalities (LMIs)

References

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APA Style

Yuan He, Jintian Hu, Shuxia Wang, Liansheng Zhang. (2019). On Delay-Range-Dependent and Delay-Rate-Dependent Stability for Delayed Systems. Control Science and Engineering, 3(2), 20-28. https://doi.org/10.11648/j.cse.20190302.11

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ACS Style

Yuan He; Jintian Hu; Shuxia Wang; Liansheng Zhang. On Delay-Range-Dependent and Delay-Rate-Dependent Stability for Delayed Systems. Control Sci. Eng. 2019, 3(2), 20-28. doi: 10.11648/j.cse.20190302.11

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AMA Style

Yuan He, Jintian Hu, Shuxia Wang, Liansheng Zhang. On Delay-Range-Dependent and Delay-Rate-Dependent Stability for Delayed Systems. Control Sci Eng. 2019;3(2):20-28. doi: 10.11648/j.cse.20190302.11

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@article{10.11648/j.cse.20190302.11,
  author = {Yuan He and Jintian Hu and Shuxia Wang and Liansheng Zhang},
  title = {On Delay-Range-Dependent and Delay-Rate-Dependent Stability for Delayed Systems},
  journal = {Control Science and Engineering},
  volume = {3},
  number = {2},
  pages = {20-28},
  doi = {10.11648/j.cse.20190302.11},
  url = {https://doi.org/10.11648/j.cse.20190302.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.cse.20190302.11},
  abstract = {It is well known that the phenomena of time delays are frequently encountered in many process and various control systems. The presence of delays can have an effect on system stability and performance, so ignoring them may lead to design flaws and incorrect analysis conclusions. Hence, the stability problem for time-delayed systems has received considerable attention in recent years. This brief focuses on the stability analysis for a class of delayed linear systems. Firstly, we construct a novel augmented Lyapunov-Krasovskii functional (LKF) which includes the lower, the upper bounds of the delay and the delay itself. Secondly, utilizing some integral inequalities and the reciprocally convex combination lemma, we obtain less conservative stability criteria formulated in form of linear matrix inequalities (LMIs). Finally, numerical examples are provided to show the effectiveness of the proposed method.},
 year = {2019}
}

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TY  - JOUR
T1  - On Delay-Range-Dependent and Delay-Rate-Dependent Stability for Delayed Systems
AU  - Yuan He
AU  - Jintian Hu
AU  - Shuxia Wang
AU  - Liansheng Zhang
Y1  - 2019/10/28
PY  - 2019
N1  - https://doi.org/10.11648/j.cse.20190302.11
DO  - 10.11648/j.cse.20190302.11
T2  - Control Science and Engineering
JF  - Control Science and Engineering
JO  - Control Science and Engineering
SP  - 20
EP  - 28
PB  - Science Publishing Group
SN  - 2994-7421
UR  - https://doi.org/10.11648/j.cse.20190302.11
AB  - It is well known that the phenomena of time delays are frequently encountered in many process and various control systems. The presence of delays can have an effect on system stability and performance, so ignoring them may lead to design flaws and incorrect analysis conclusions. Hence, the stability problem for time-delayed systems has received considerable attention in recent years. This brief focuses on the stability analysis for a class of delayed linear systems. Firstly, we construct a novel augmented Lyapunov-Krasovskii functional (LKF) which includes the lower, the upper bounds of the delay and the delay itself. Secondly, utilizing some integral inequalities and the reciprocally convex combination lemma, we obtain less conservative stability criteria formulated in form of linear matrix inequalities (LMIs). Finally, numerical examples are provided to show the effectiveness of the proposed method.
VL  - 3
IS  - 2
ER  -

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Author Information

Yuan He

Deparment of Automation, Beijing Institute of Petro-chemical Technology, Beijing, China
Jintian Hu

Deparment of Automation, Beijing Institute of Petro-chemical Technology, Beijing, China
Shuxia Wang

Deparment of Mathematics and Physics, Beijing Institute of Petro-chemical Technology, Beijing, China
Liansheng Zhang

Deparment of Mathematics and Physics, Beijing Institute of Petro-chemical Technology, Beijing, China

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Plain Text BibTeX RIS

APA Style

Yuan He, Jintian Hu, Shuxia Wang, Liansheng Zhang. (2019). On Delay-Range-Dependent and Delay-Rate-Dependent Stability for Delayed Systems. Control Science and Engineering, 3(2), 20-28. https://doi.org/10.11648/j.cse.20190302.11

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ACS Style

Yuan He; Jintian Hu; Shuxia Wang; Liansheng Zhang. On Delay-Range-Dependent and Delay-Rate-Dependent Stability for Delayed Systems. Control Sci. Eng. 2019, 3(2), 20-28. doi: 10.11648/j.cse.20190302.11

Copy | Download

AMA Style

Yuan He, Jintian Hu, Shuxia Wang, Liansheng Zhang. On Delay-Range-Dependent and Delay-Rate-Dependent Stability for Delayed Systems. Control Sci Eng. 2019;3(2):20-28. doi: 10.11648/j.cse.20190302.11

Copy | Download

@article{10.11648/j.cse.20190302.11,
  author = {Yuan He and Jintian Hu and Shuxia Wang and Liansheng Zhang},
  title = {On Delay-Range-Dependent and Delay-Rate-Dependent Stability for Delayed Systems},
  journal = {Control Science and Engineering},
  volume = {3},
  number = {2},
  pages = {20-28},
  doi = {10.11648/j.cse.20190302.11},
  url = {https://doi.org/10.11648/j.cse.20190302.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.cse.20190302.11},
  abstract = {It is well known that the phenomena of time delays are frequently encountered in many process and various control systems. The presence of delays can have an effect on system stability and performance, so ignoring them may lead to design flaws and incorrect analysis conclusions. Hence, the stability problem for time-delayed systems has received considerable attention in recent years. This brief focuses on the stability analysis for a class of delayed linear systems. Firstly, we construct a novel augmented Lyapunov-Krasovskii functional (LKF) which includes the lower, the upper bounds of the delay and the delay itself. Secondly, utilizing some integral inequalities and the reciprocally convex combination lemma, we obtain less conservative stability criteria formulated in form of linear matrix inequalities (LMIs). Finally, numerical examples are provided to show the effectiveness of the proposed method.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - On Delay-Range-Dependent and Delay-Rate-Dependent Stability for Delayed Systems
AU  - Yuan He
AU  - Jintian Hu
AU  - Shuxia Wang
AU  - Liansheng Zhang
Y1  - 2019/10/28
PY  - 2019
N1  - https://doi.org/10.11648/j.cse.20190302.11
DO  - 10.11648/j.cse.20190302.11
T2  - Control Science and Engineering
JF  - Control Science and Engineering
JO  - Control Science and Engineering
SP  - 20
EP  - 28
PB  - Science Publishing Group
SN  - 2994-7421
UR  - https://doi.org/10.11648/j.cse.20190302.11
AB  - It is well known that the phenomena of time delays are frequently encountered in many process and various control systems. The presence of delays can have an effect on system stability and performance, so ignoring them may lead to design flaws and incorrect analysis conclusions. Hence, the stability problem for time-delayed systems has received considerable attention in recent years. This brief focuses on the stability analysis for a class of delayed linear systems. Firstly, we construct a novel augmented Lyapunov-Krasovskii functional (LKF) which includes the lower, the upper bounds of the delay and the delay itself. Secondly, utilizing some integral inequalities and the reciprocally convex combination lemma, we obtain less conservative stability criteria formulated in form of linear matrix inequalities (LMIs). Finally, numerical examples are provided to show the effectiveness of the proposed method.
VL  - 3
IS  - 2
ER  -

Copy | Download