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Membership Function Derivatives Transformation Approach for Stability Analysis and Stabilization Control of T-S Fuzzy Systems

Research output: Contribution to journalArticlepeer-review

He Li, Wen bo Xie, Hak Keung Lam, Jian Zhang

Original languageEnglish
JournalIEEE Transactions on Cybernetics
Accepted/In press2021


King's Authors


In this text, a membership function derivatives (MFDs) extrema-based method is proposed to relax the conservatism both in stability analysis and synthesis problems of Takagi-Sugeno fuzzy systems. By the designed algorithm, the nonpositiveness of the MFDs extrema is conquered. For an open-loop system, based on certain information of the MFs and derivatives, a series of convex stability conditions is derived. Then, an extremum-based construction method is adopted to involve the MF information. For the shape of MFDs, a coordinate transformation algorithm is proposed to involve it in the stability conditions to achieve local stable effects. For a state-feedback control system, conditions guaranteeing the stability and robustness are listed. Finally, simulation examples and comparisons are carried out to clarify the conservatism reduction results of the raised method.

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