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Stability analysis of discrete‐time switched positive linear systems with unstable subsystem.

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Title: Stability analysis of discrete‐time switched positive linear systems with unstable subsystem.
Authors: Liu, Li‐Juan1 (AUTHOR) liulj@djtu.edu.cn, Zhang, Zhao2 (AUTHOR), Karimi, Hamid Reza3 (AUTHOR), Chen, Shu Yue2 (AUTHOR)
Source: Asian Journal of Control. Jul2025, Vol. 27 Issue 4, p1964-1974. 11p.
Subjects: Positive systems, Linear systems, Lyapunov functions, Lyapunov stability, Linear statistical models
Abstract: This paper deals with the problem of stability analysis for discrete‐time switched positive linear systems with unstable subsystems. The fundamental concept involves utilizing the stability properties of switching behavior to counteract the state divergence introduced by unstable systems. Moreover, the existing results in the literature lack a method that can simultaneously address the stability analysis of switching positive systems containing only stable subsystems or containing unstable subsystems or only unstable subsystems. Therefore, in this paper, based on the widely used discretization Lyapunov function method in time‐delay systems, a new dwell‐time dependent co‐positive Lyapunov function was proposed by applying it to switched positive systems. A computable sufficient condition for stability analysis of switched linear systems with unstable subsystems was established within the dwell time framework. To verify the effectiveness of the results, this paper provides a numerical example and an example of supersaturated cross signal control for illustration, as well. [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: Stability analysis of discrete‐time switched positive linear systems with unstable subsystem.
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  Data: <searchLink fieldCode="AR" term="%22Liu%2C+Li‐Juan%22">Liu, Li‐Juan</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> liulj@djtu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Zhang%2C+Zhao%22">Zhang, Zhao</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Karimi%2C+Hamid+Reza%22">Karimi, Hamid Reza</searchLink><relatesTo>3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Chen%2C+Shu+Yue%22">Chen, Shu Yue</searchLink><relatesTo>2</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Asian+Journal+of+Control%22">Asian Journal of Control</searchLink>. Jul2025, Vol. 27 Issue 4, p1964-1974. 11p.
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  Data: <searchLink fieldCode="DE" term="%22Positive+systems%22">Positive systems</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+systems%22">Linear systems</searchLink><br /><searchLink fieldCode="DE" term="%22Lyapunov+functions%22">Lyapunov functions</searchLink><br /><searchLink fieldCode="DE" term="%22Lyapunov+stability%22">Lyapunov stability</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+statistical+models%22">Linear statistical models</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This paper deals with the problem of stability analysis for discrete‐time switched positive linear systems with unstable subsystems. The fundamental concept involves utilizing the stability properties of switching behavior to counteract the state divergence introduced by unstable systems. Moreover, the existing results in the literature lack a method that can simultaneously address the stability analysis of switching positive systems containing only stable subsystems or containing unstable subsystems or only unstable subsystems. Therefore, in this paper, based on the widely used discretization Lyapunov function method in time‐delay systems, a new dwell‐time dependent co‐positive Lyapunov function was proposed by applying it to switched positive systems. A computable sufficient condition for stability analysis of switched linear systems with unstable subsystems was established within the dwell time framework. To verify the effectiveness of the results, this paper provides a numerical example and an example of supersaturated cross signal control for illustration, as well. [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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      – Type: doi
        Value: 10.1002/asjc.3562
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      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 11
        StartPage: 1964
    Subjects:
      – SubjectFull: Positive systems
        Type: general
      – SubjectFull: Linear systems
        Type: general
      – SubjectFull: Lyapunov functions
        Type: general
      – SubjectFull: Lyapunov stability
        Type: general
      – SubjectFull: Linear statistical models
        Type: general
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      – TitleFull: Stability analysis of discrete‐time switched positive linear systems with unstable subsystem.
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            NameFull: Liu, Li‐Juan
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            NameFull: Zhang, Zhao
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            NameFull: Karimi, Hamid Reza
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            NameFull: Chen, Shu Yue
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          Dates:
            – D: 01
              M: 07
              Text: Jul2025
              Type: published
              Y: 2025
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              Value: 27
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              Value: 4
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            – TitleFull: Asian Journal of Control
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