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

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), 2019. Published by Science Publishing Group

Keywords

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

References
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Cite This Article
  • 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
  • Deparment of Automation, Beijing Institute of Petro-chemical Technology, Beijing, China

  • Deparment of Automation, Beijing Institute of Petro-chemical Technology, Beijing, China

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

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

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