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Admissibility and stabilization of descriptor T–S fuzzy systems with two additive time-varying delays

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Abstract

This paper discusses the problems of admissibility and stabilization of descriptor T–S fuzzy systems with two additive time-varying delays. Firstly, new delay-dependent conditions are derived by applying a generalized free matrix based on Bessel–Legendre inequality, by constructing an appropriate Lyapunov–Krasovskii functional and by introducing some slack variables in order to reduce the conservatism and to give more relaxation to the considered system. Then, and based on the established admissibility conditions, a fuzzy controller criterion is designed to ensure the regularity, the impulse-free, and the asymptotic stability of the descriptor T–S fuzzy systems with time-varying delay. All the proposed conditions and criteria are expressed in terms of linear matrix inequalities. Finally, some numerical and practical examples are provided to demonstrate the effectiveness and the applicability of the proposed method and to compare the obtained results with some existing ones in the literature.

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Data availability

The data that support the findings of this study are available from the corresponding author, [author initials], upon reasonable request.

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Funding

The authors did not receive support from any organization for the submitted work. The authors have no relevant financial or nonfinancial interests to disclose.

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Authors and Affiliations

  1. Laboratory LISAC, Department of physics, Faculty of Sciences Dhar El Mehraz, Sidi Mohamed Ben Abdellah University, BP 1976 Fez Atlas, 30000, Fez, Morocco

    Driss El-Jimi, Noreddine Chaibi, Ismail Boumhidi & Mohammed Charqi

Authors
  1. Driss El-Jimi
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  2. Noreddine Chaibi
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  3. Ismail Boumhidi
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  4. Mohammed Charqi
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Contributions

E-JD, CN: Conception—Constructing an idea or hypothesis for overarching research goals and aims. E-JD, CN, CM: Methodology—Development or design of methodology; creation of models. E-JD: Software—Programming, software development; designing computer programs; implementation of the computer code and supporting algorithms; testing of existing code components. CN, BI, CM: Validation—Verification, whether as a part of the activity or separate, of the overall replication/reproducibility of results/experiments and other research outputs. E-JD, CN, CM: Formal analysis—Application of statistical, mathematical, computational, or other formal techniques to analyze or synthesize study data. E-JD, CN, CM: Investigation—Conducting a research and investigation process, specifically performing the experiments, or data/evidence collection. BI: Resources—Provision of study materials, reagents, materials, patients, laboratory samples, computing resources, or other analysis tools. E-JD, CN, BI, CM: Data Curation—Management activities to annotate (produce metadata), scrub data and maintain research data (including software code, where it is necessary for interpreting the data itself) for initial use and later reuse. E-JD, BI, CM: Writing—original draft preparation—Creation and/or presentation of the published work, specifically writing the initial draft (including substantive translation). CN, BI, CM: Writing—review and editing—Preparation, creation and/or presentation of the published work by those from the original research group, specifically critical review, commentary or revision—including pre- or post-publication stages. CN, CM: Visualization—Preparation, creation and/or presentation of the published work, specifically visualization/data presentation. BI: Supervision—Oversight and leadership responsibility for the research activity planning and execution, including mentorship external to the core team. CN, BI: Project administration—Management and coordination responsibility for the research activity planning and execution.

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Correspondence to Driss El-Jimi.

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El-Jimi, D., Chaibi, N., Boumhidi, I. et al. Admissibility and stabilization of descriptor T–S fuzzy systems with two additive time-varying delays. Int. J. Dynam. Control 11, 2438–2451 (2023). https://doi.org/10.1007/s40435-023-01136-2

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