T-S fuzzy bilinear model and fuzzy controller design for a class of nonlinear systems

Tzuu-Hseng S. Li, Shun Hung Tsai

Research output: Contribution to journalArticlepeer-review

134 Citations (Scopus)


This paper proposes a fuzzy bilinear model for a class of nonlinear systems and a fuzzy controller to stabilize such systems. By examination of a modeling problem, we describe how to transform a nonlinear system into a bilinear one via Taylor's series expansion and then we adopt the Takagi-Sugeno (T-S) fuzzy modeling technique to construct a fuzzy bilinear model. For controller design, the parallel distributed compensation (PDC) method is utilized to stabilize the fuzzy bilinear system (FBS), and some sufficient conditions are derived to guarantee the stability of the overall fuzzy control system via linear matrix inequalities (LMIs). Moreover, we propound some sufficient conditions for robust stabilization of the FBS with parametric uncertainties. Finally, a numerical example and the Van de Vusse model are utilized to demonstrate the validity and effectiveness of the proposed FBS.

Original languageEnglish
Pages (from-to)494-506
Number of pages13
JournalIEEE Transactions on Fuzzy Systems
Issue number3
Publication statusPublished - 2007 Jun 1

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computational Theory and Mathematics
  • Artificial Intelligence
  • Applied Mathematics

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