A New Fuzzy Lyapunov Function for Relaxed Stability Condition of Continuous-Time Takagi–Sugeno Fuzzy Systems

  • Authors:
  • Dong Hwan Lee; Jin Bae Park; Young Hoon Joo

  • Affiliations:
  • Dept. of Electr. Eng., Yonsei Univ., Seoul, South Korea;-;-

  • Venue:
  • IEEE Transactions on Fuzzy Systems
  • Year:
  • 2011

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Abstract

This paper presents a new fuzzy Lyapunov function (FLF) for the stability analysis of continuous-time Takagi-Sugeno (T-S) fuzzy systems. Unlike conventional FLFs, the proposed one depends not only on the fuzzy weighting functions of the T-S fuzzy systems but on their first-order time derivatives as well. Based on the proposed FLF, a sufficient stability condition is derived in the form of linear matrix inequalities, depending on the upper bounds on the second-order time derivative of the fuzzy weighting functions, as well as the first-order ones. Finally, some examples demonstrate that the proposed condition can provide less conservative results than the previous ones in the literature.