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Lyapunov stability of nonlinear systems with delayed impulses: An event‐triggered impulsive control approach.

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Title: Lyapunov stability of nonlinear systems with delayed impulses: An event‐triggered impulsive control approach.
Authors: Shang, Bing1 (AUTHOR), Zhang, Jin‐E1 (AUTHOR) zhang86021205@163.com, Wu, Ailong1 (AUTHOR)
Source: Asian Journal of Control. Sep2026, Vol. 28 Issue 5, p2236-2246. 11p.
Subjects: Lyapunov stability, Nonlinear systems, Linear matrix inequalities, Control theory (Engineering), Global asymptotic stability, Discrete systems
Abstract: In this paper, we employ an event‐triggered impulsive control (ETIC) approach to examine the Lyapunov stability of nonlinear systems subject to delayed impulses. Leveraging impulse control theory, an event‐triggered mechanism (ETM) based on the Lyapunov function is developed, and sufficient conditions are established to ensure both uniform stability (US) and global asymptotic stability (GAS) of the considered system while excluding Zeno behavior. It has been shown that the stability conditions depend not only on the ETM but also on time delays. Subsequently, we apply these theoretical findings to a nonlinear impulsive control system and design the appropriate ETM and impulse controllers according to the linear matrix inequality (LMI) to realize the GAS. The controller accounts for the impact of delays and is activated solely upon event triggering. Finally, two numerical simulations are shown to confirm the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]
Copyright of Asian Journal of Control is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Lyapunov stability of nonlinear systems with delayed impulses: An event‐triggered impulsive control approach.
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  Data: <searchLink fieldCode="AR" term="%22Shang%2C+Bing%22">Shang, Bing</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Zhang%2C+Jin‐E%22">Zhang, Jin‐E</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> zhang86021205@163.com</i><br /><searchLink fieldCode="AR" term="%22Wu%2C+Ailong%22">Wu, Ailong</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Asian+Journal+of+Control%22">Asian Journal of Control</searchLink>. Sep2026, Vol. 28 Issue 5, p2236-2246. 11p.
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  Data: <searchLink fieldCode="DE" term="%22Lyapunov+stability%22">Lyapunov stability</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+systems%22">Nonlinear systems</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+matrix+inequalities%22">Linear matrix inequalities</searchLink><br /><searchLink fieldCode="DE" term="%22Control+theory+%28Engineering%29%22">Control theory (Engineering)</searchLink><br /><searchLink fieldCode="DE" term="%22Global+asymptotic+stability%22">Global asymptotic stability</searchLink><br /><searchLink fieldCode="DE" term="%22Discrete+systems%22">Discrete systems</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: In this paper, we employ an event‐triggered impulsive control (ETIC) approach to examine the Lyapunov stability of nonlinear systems subject to delayed impulses. Leveraging impulse control theory, an event‐triggered mechanism (ETM) based on the Lyapunov function is developed, and sufficient conditions are established to ensure both uniform stability (US) and global asymptotic stability (GAS) of the considered system while excluding Zeno behavior. It has been shown that the stability conditions depend not only on the ETM but also on time delays. Subsequently, we apply these theoretical findings to a nonlinear impulsive control system and design the appropriate ETM and impulse controllers according to the linear matrix inequality (LMI) to realize the GAS. The controller accounts for the impact of delays and is activated solely upon event triggering. Finally, two numerical simulations are shown to confirm the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Asian Journal of Control is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1002/asjc.3813
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 11
        StartPage: 2236
    Subjects:
      – SubjectFull: Lyapunov stability
        Type: general
      – SubjectFull: Nonlinear systems
        Type: general
      – SubjectFull: Linear matrix inequalities
        Type: general
      – SubjectFull: Control theory (Engineering)
        Type: general
      – SubjectFull: Global asymptotic stability
        Type: general
      – SubjectFull: Discrete systems
        Type: general
    Titles:
      – TitleFull: Lyapunov stability of nonlinear systems with delayed impulses: An event‐triggered impulsive control approach.
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            NameFull: Shang, Bing
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            NameFull: Zhang, Jin‐E
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            NameFull: Wu, Ailong
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          Dates:
            – D: 01
              M: 09
              Text: Sep2026
              Type: published
              Y: 2026
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              Value: 28
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              Value: 5
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            – TitleFull: Asian Journal of Control
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