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Relaxed Controller Design Conditions for Takagi–Sugeno Systems with State Time-Varying Delays

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Abstract

This paper deals with the design of fuzzy controllers for Takagi–Sugeno (T-S) fuzzy models with state time-varying delays. New relaxed delay-dependent conditions for the stabilization purpose are proposed in terms of linear matrix inequalities (LMIs), including the knowledge of the bounds of the time-varying delay and its rate of variation. The conservatism improvement is brought through three points: (1) the choice of a convenient augmented Lyapunov–Krasovskii functional candidate, (2) the application of an extension of the Jensen’s inequality, and (3) the Finsler’s lemma. In this context, a parallel distributed compensation control law, which includes both memoryless and delayed state feedbacks, is considered. To apply such control law, it is required to assume that the time-varying delay is available online. Under this assumption, it is highlighted that the proposed LMI-based conditions are significantly relaxed for high rate of variation of the time delay. On the other hand, when this assumption cannot be guaranteed, straightforward corollaries are proposed. A numerical example is provided to illustrate the effectiveness of the proposed LMI-based conditions and their conservatism improvement regarding to previous results.

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Acknowledgments

The authors would like to thanks the reviewers and Ms. Adèle Ayed for their valuable comments within this study.

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Authors and Affiliations

  1. CReSTIC EA3804, University of Reims Champagne-Ardenne, BP1034, 51687, Reims Cedex, France

    Fayçal Bourahala, Kevin Guelton & Noureddine Manamanni

  2. QUERE Laboratory, Engineering Faculty, University of Setif 1, 19000, Setif, Algeria

    Fayçal Bourahala & Farid Khaber

Authors
  1. Fayçal Bourahala
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  2. Kevin Guelton
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  3. Noureddine Manamanni
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  4. Farid Khaber
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Correspondence to Kevin Guelton.

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Bourahala, F., Guelton, K., Manamanni, N. et al. Relaxed Controller Design Conditions for Takagi–Sugeno Systems with State Time-Varying Delays. Int. J. Fuzzy Syst. 19, 1406–1416 (2017). https://doi.org/10.1007/s40815-016-0267-9

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  • DOI: https://doi.org/10.1007/s40815-016-0267-9

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