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Stability analysis and control of two-dimensional fuzzy systems with directional time-varying delays

journal contribution
posted on 2018-06-01, 00:00 authored by Hien Le, Hieu TrinhHieu Trinh
This paper is concerned with the problem of stability and stabilization of wo-dimensional (2-D) Takagi-Sugeno fuzzy systems described by the Roesser model with state delays. The directional state delays are unknown and time-varying which belong to certain ranges with known upper and lower bounds. The common center-average defuzzifier approach is first utilized to present the defuzzified output dynamics of 2-D fuzzy rule-based systems. Then, in light of a 2-D Lyapunov-like scheme, we construct a suitable augmented fuzzy parameter-dependent Lyapunov functional candidate to establish stability conditions for the open-loop system. Based on some novel 2-D summation inequalities, which generalize the ones based on Wirtinger inequality, Abel lemma or Cauchy-Schwarz inequality, and by utilizing a reciprocally convex combination technique, delay-dependent stability conditions are derived in terms of tractable linear matrix inequalities (LMIs). The obtained results on stability analysis are then utilized to address the problem of designing a rule-based state feedback controller that makes the 2-D fuzzy closed-loop system stable. The effectiveness and advantage of the obtained results is illustrated through numerical examples.

History

Journal

IEEE Transactions on Fuzzy Systems

Volume

PP

Issue

99

Pagination

1 - 14

Publisher

Institute of Electrical and Electronics Engineers (IEEE)

Location

Piscataway, N.J.

ISSN

1063-6706

Language

eng

Publication classification

C Journal article; C1 Refereed article in a scholarly journal

Copyright notice

2017, IEEE