Robust Admissibility of Uncertain T–S Fuzzy Singular Systems with Time-Varying Delay: An Input–Output Approach

This article discusses the problems of admissibility for uncertain T–S fuzzy singular systems with time-varying delay. Firstly, a model which transforms the original system into two interconnected systems by two-term approximation of the delayed state based on small gain theorem is proposed. Then, t...

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Published in:Journal of control, automation & electrical systems Vol. 34; no. 5; pp. 951 - 962
Main Authors: El-Jimi, Driss, Chaibi, Noreddine, Boumhidi, Ismail, Charqi, Mohammed
Format: Journal Article
Language:English
Published: New York Springer US 01.10.2023
Springer Nature B.V
Subjects:
Approximation
Control
Control and Systems Theory
Electrical Engineering
Engineering
Fuzzy sets
Inequality
Linear matrix inequalities
Mechatronics
Robotics
Robotics and Automation
Input–output approach
Asymptotic stability
Takagi–Sugeno fuzzy model
Singular systems
Time-varying delay
Lyapunov–Krasovskii function
ISSN:2195-3880, 2195-3899
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Abstract This article discusses the problems of admissibility for uncertain T–S fuzzy singular systems with time-varying delay. Firstly, a model which transforms the original system into two interconnected systems by two-term approximation of the delayed state based on small gain theorem is proposed. Then, the generalized integral inequality method is used to derive the admissibility conditions for uncertain T–S fuzzy singular systems. Moreover, to account for the generalized integral inequality, new augmented Lyapunov–Krasovskii functional is constructed with some new terms. Consequently, the developed criteria are given in terms of linear matrix inequalities “LMIs,” which provide less conservative results than some recent existing ones in the literature. Finally, numerical examples are given to demonstrate the applicability and the effectiveness of the developed method in this article.
AbstractList This article discusses the problems of admissibility for uncertain T–S fuzzy singular systems with time-varying delay. Firstly, a model which transforms the original system into two interconnected systems by two-term approximation of the delayed state based on small gain theorem is proposed. Then, the generalized integral inequality method is used to derive the admissibility conditions for uncertain T–S fuzzy singular systems. Moreover, to account for the generalized integral inequality, new augmented Lyapunov–Krasovskii functional is constructed with some new terms. Consequently, the developed criteria are given in terms of linear matrix inequalities “LMIs,” which provide less conservative results than some recent existing ones in the literature. Finally, numerical examples are given to demonstrate the applicability and the effectiveness of the developed method in this article.
Author Boumhidi, Ismail
Charqi, Mohammed
El-Jimi, Driss
Chaibi, Noreddine
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  fullname: Charqi, Mohammed
  organization: Department of Physics, LISAC, Faculty of Sciences Dhar El Mehraz, Sidi Mohamed Ben Abdellah University
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CitedBy_id crossref_primary_10_1007_s40435_024_01448_x
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Issue 5
Keywords Input–output approach
Asymptotic stability
Takagi–Sugeno fuzzy model
Singular systems
Time-varying delay
Lyapunov–Krasovskii function
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Snippet This article discusses the problems of admissibility for uncertain T–S fuzzy singular systems with time-varying delay. Firstly, a model which transforms the...
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StartPage 951
SubjectTerms Approximation
Control
Control and Systems Theory
Electrical Engineering
Engineering
Fuzzy sets
Inequality
Linear matrix inequalities
Mechatronics
Robotics
Robotics and Automation
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Title Robust Admissibility of Uncertain T–S Fuzzy Singular Systems with Time-Varying Delay: An Input–Output Approach
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