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On Stability and Stabilization of T–S Fuzzy Systems With Time-Varying Delays via Quadratic Fuzzy Lyapunov Matrix.

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Title: On Stability and Stabilization of T–S Fuzzy Systems With Time-Varying Delays via Quadratic Fuzzy Lyapunov Matrix.
Authors: Li, Guiling1 (AUTHOR) liguiling1123@126.com, Peng, Chen1 (AUTHOR) c.peng@shu.edu.cn, Xie, Xiangpeng2 (AUTHOR) xiexiangpeng1953@163.com, Xie, Shaorong3 (AUTHOR) srxie@shu.edu.cn
Source: IEEE Transactions on Fuzzy Systems. Sep2022, Vol. 30 Issue 9, p3762-3773. 12p.
Subjects: Time-varying systems, Fuzzy systems, Integral inequalities, Stability criterion, Linear matrix inequalities, Membership functions (Fuzzy logic)
Abstract: This article proposes improved stability and stabilization criteria for Takagi–Sugeno (T–S) fuzzy systems with time-varying delays. First, a novel augmented fuzzy Lyapunov–Krasovskii functional (LKF) including the quadratic fuzzy Lyapunov matrix is constructed, which can provide much information of T–S fuzzy systems and help to achieve the lager allowable delay upper bounds. Then, improved delay-dependent stability and stabilization criteria are derived for the studied systems. Compared with the traditional methods, since the third-order Bessel–Legendre inequality and the extended reciprocally convex matrix inequality are well employed in the derivative of the constructed LKF to give tighter bounds of the single integral terms, the conservatism of derived criteria is further reduced. In addition, the quadratic fuzzy Lyapunov matrix introduced in LKF, which contains the quadratic membership functions, is also an important reason for obtaining less conservative results. Finally, numerical examples demonstrate that the proposed method is less conservative than some existing ones and the studied system can be well controlled by the designed controller. [ABSTRACT FROM AUTHOR]
Copyright of IEEE Transactions on Fuzzy Systems is the property of IEEE 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: On Stability and Stabilization of T–S Fuzzy Systems With Time-Varying Delays via Quadratic Fuzzy Lyapunov Matrix.
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  Data: <searchLink fieldCode="JN" term="%22IEEE+Transactions+on+Fuzzy+Systems%22">IEEE Transactions on Fuzzy Systems</searchLink>. Sep2022, Vol. 30 Issue 9, p3762-3773. 12p.
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  Data: <searchLink fieldCode="DE" term="%22Time-varying+systems%22">Time-varying systems</searchLink><br /><searchLink fieldCode="DE" term="%22Fuzzy+systems%22">Fuzzy systems</searchLink><br /><searchLink fieldCode="DE" term="%22Integral+inequalities%22">Integral inequalities</searchLink><br /><searchLink fieldCode="DE" term="%22Stability+criterion%22">Stability criterion</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+matrix+inequalities%22">Linear matrix inequalities</searchLink><br /><searchLink fieldCode="DE" term="%22Membership+functions+%28Fuzzy+logic%29%22">Membership functions (Fuzzy logic)</searchLink>
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  Data: This article proposes improved stability and stabilization criteria for Takagi–Sugeno (T–S) fuzzy systems with time-varying delays. First, a novel augmented fuzzy Lyapunov–Krasovskii functional (LKF) including the quadratic fuzzy Lyapunov matrix is constructed, which can provide much information of T–S fuzzy systems and help to achieve the lager allowable delay upper bounds. Then, improved delay-dependent stability and stabilization criteria are derived for the studied systems. Compared with the traditional methods, since the third-order Bessel–Legendre inequality and the extended reciprocally convex matrix inequality are well employed in the derivative of the constructed LKF to give tighter bounds of the single integral terms, the conservatism of derived criteria is further reduced. In addition, the quadratic fuzzy Lyapunov matrix introduced in LKF, which contains the quadratic membership functions, is also an important reason for obtaining less conservative results. Finally, numerical examples demonstrate that the proposed method is less conservative than some existing ones and the studied system can be well controlled by the designed controller. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
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  Data: <i>Copyright of IEEE Transactions on Fuzzy Systems is the property of IEEE 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: 10.1109/TFUZZ.2021.3128062
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      – Code: eng
        Text: English
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        PageCount: 12
        StartPage: 3762
    Subjects:
      – SubjectFull: Time-varying systems
        Type: general
      – SubjectFull: Fuzzy systems
        Type: general
      – SubjectFull: Integral inequalities
        Type: general
      – SubjectFull: Stability criterion
        Type: general
      – SubjectFull: Linear matrix inequalities
        Type: general
      – SubjectFull: Membership functions (Fuzzy logic)
        Type: general
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      – TitleFull: On Stability and Stabilization of T–S Fuzzy Systems With Time-Varying Delays via Quadratic Fuzzy Lyapunov Matrix.
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            NameFull: Li, Guiling
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            NameFull: Peng, Chen
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            NameFull: Xie, Shaorong
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            – D: 01
              M: 09
              Text: Sep2022
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              Y: 2022
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