Polynomial Controller Synthesis for Uncertain Large-Scale Polynomial T-S Fuzzy Systems

Van Phong Vu, Wen June Wang

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


This paper proposes a novel method to synthesize a controller for stabilizing the nonlinear large-scale system which is represented by a large-scale polynomial Takagi-Sugeno (T-S) fuzzy system. The large-scale system consists of a set of the uncertain polynomial T-S fuzzy system with interconnection terms. Modeling the large-scale nonlinear system under the framework of the polynomial form will decrease both the modeling errors and the number of fuzzy rules with respect to the conventional large-scale T-S fuzzy system. In addition, because of the existence of uncertainties, the synthesizing controller for the large-scale polynomial fuzzy system becomes much more challenging and has not been investigated in the previous studies. In this paper, a controller is synthesized to simultaneously eliminate the impact of the uncertainties and stabilize the system. With the aid of Lyapunov theory, sum-of-square technique, and S-procedure, the conditions for controller synthesis are derived in the main theorems. Finally, two examples are illustrated to show the effectiveness and merit of the proposed method.

Original languageEnglish
Article number8638850
Pages (from-to)1929-1942
Number of pages14
JournalIEEE Transactions on Cybernetics
Issue number4
StatePublished - Apr 2021


  • Decentralized controller synthesis
  • large-scale polynomial Takagi-Sugeno (T-S) fuzzy system
  • large-scale systems
  • sum-of-square (SOS)
  • uncertainties


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