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Delay-variation-dependent summation inequality and its application to stability analysis of discrete-time systems with time-varying delay.

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Title: Delay-variation-dependent summation inequality and its application to stability analysis of discrete-time systems with time-varying delay.
Authors: Wang, Chen-Rui (AUTHOR), He, Yong1 (AUTHOR) heyong08@cug.edu.cn, Zhang, Chuan-Ke (AUTHOR), Chen, Wen-Hu (AUTHOR), Wu, Min (AUTHOR)
Source: Systems & Control Letters. Feb2024, Vol. 184, pN.PAG-N.PAG. 1p.
Subjects: Discrete-time systems, Time-varying systems, Stability criterion, Conservatism, Linear matrix inequalities
Abstract: This work tends to research the stability of the discrete-time systems with a time-varying delay based on the Lyapunov-Krasovskii functional (LKF) method. In order to acquire a less conservative stability criterion, some techniques in this work are refined and taken into use. Firstly, to reduce the conservatism generated when estimating the forward difference of the LKF, a newly delay-variation-dependent summation inequality is constructed, which includes the existing free-matrix-based and Bessel function-based summation inequalities, using delay-variation-product relaxed matrices to provide more freedom for the estimation results. Secondly, to further show the influence of the introduced variation information in the time-varying delay, we give another selection of the allowable delay set for the delayed discrete-time systems. Thirdly, by taking advantages of the above method and by constructing a delay-product-type LKF, using extended free-weighting-matrices zero equations, and considering different allowable delay sets, two improved linear matrix inequality (LMI)-based delay-variation-dependent criteria for delayed discrete-time systems are formulated. Some classical numerical instances are presented to explain the effectiveness of these proposed stability criteria. [ABSTRACT FROM AUTHOR]
Copyright of Systems & Control Letters is the property of Elsevier B.V. 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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DbLabel: Engineering Source
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  Data: Delay-variation-dependent summation inequality and its application to stability analysis of discrete-time systems with time-varying delay.
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  Data: <searchLink fieldCode="AR" term="%22Wang%2C+Chen-Rui%22">Wang, Chen-Rui</searchLink> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22He%2C+Yong%22">He, Yong</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> heyong08@cug.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Zhang%2C+Chuan-Ke%22">Zhang, Chuan-Ke</searchLink> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Chen%2C+Wen-Hu%22">Chen, Wen-Hu</searchLink> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Wu%2C+Min%22">Wu, Min</searchLink> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Systems+%26+Control+Letters%22">Systems & Control Letters</searchLink>. Feb2024, Vol. 184, pN.PAG-N.PAG. 1p.
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  Data: <searchLink fieldCode="DE" term="%22Discrete-time+systems%22">Discrete-time systems</searchLink><br /><searchLink fieldCode="DE" term="%22Time-varying+systems%22">Time-varying systems</searchLink><br /><searchLink fieldCode="DE" term="%22Stability+criterion%22">Stability criterion</searchLink><br /><searchLink fieldCode="DE" term="%22Conservatism%22">Conservatism</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+matrix+inequalities%22">Linear matrix inequalities</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This work tends to research the stability of the discrete-time systems with a time-varying delay based on the Lyapunov-Krasovskii functional (LKF) method. In order to acquire a less conservative stability criterion, some techniques in this work are refined and taken into use. Firstly, to reduce the conservatism generated when estimating the forward difference of the LKF, a newly delay-variation-dependent summation inequality is constructed, which includes the existing free-matrix-based and Bessel function-based summation inequalities, using delay-variation-product relaxed matrices to provide more freedom for the estimation results. Secondly, to further show the influence of the introduced variation information in the time-varying delay, we give another selection of the allowable delay set for the delayed discrete-time systems. Thirdly, by taking advantages of the above method and by constructing a delay-product-type LKF, using extended free-weighting-matrices zero equations, and considering different allowable delay sets, two improved linear matrix inequality (LMI)-based delay-variation-dependent criteria for delayed discrete-time systems are formulated. Some classical numerical instances are presented to explain the effectiveness of these proposed stability criteria. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Systems & Control Letters is the property of Elsevier B.V. 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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        Value: 10.1016/j.sysconle.2024.105721
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      – Code: eng
        Text: English
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        Type: general
      – SubjectFull: Time-varying systems
        Type: general
      – SubjectFull: Stability criterion
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      – SubjectFull: Conservatism
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      – SubjectFull: Linear matrix inequalities
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      – TitleFull: Delay-variation-dependent summation inequality and its application to stability analysis of discrete-time systems with time-varying delay.
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              Text: Feb2024
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              Value: 184
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