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International Journal of Fuzzy Systems

, Volume 19, Issue 5, pp 1406–1416 | Cite as

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

  • Fayçal Bourahala
  • Kevin Guelton
  • Noureddine Manamanni
  • Farid Khaber
Article

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.

Keywords

Takagi–Sugeno (T-S) models Time-varying delay Delay-dependent controller design Lyapunov–Krasovksii functional (LKF) Linear matrix inequalities (LMIs) 

Notes

Acknowledgments

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

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Copyright information

© Taiwan Fuzzy Systems Association and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.CReSTIC EA3804 University of Reims Champagne-ArdenneReims CedexFrance
  2. 2.QUERE Laboratory, Engineering FacultyUniversity of Setif 1SetifAlgeria

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