A new stability region analysis of continuous-time Takagi-Sugeno fuzzy systems using fuzzy Lyapunov functions

In this paper, we propose a new sufficient condition in the form of eigenvalue problem (EVP) for assessing the stability of continuous-time Takagi-Sugeno (T-S) fuzzy systems and estimating the domain of attraction (DA) based on fuzzy Lyapunov functions (FLFs). In order to deal with the time-derivatives of the fuzzy weighting functions (TDFWFs) in the Lyapunov inequality, the existing conditions consider the upper bound on each TDFWF´s absolute value. The main result of this paper is derived considering an inequality constraint of a nonlinear function depending quadratically on the fuzzy weighting functions. Finally, an example is given to demonstrate the effectiveness and validity of the proposed approach.