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.