Domain of attraction analysis for continuous-time Takagi-Sugeno fuzzy systems: An LMI approach

This paper proposes a strategy to estimate invariant subsets of the domain of attraction (DA) for continuous-time Takagi-Sugeno (T-S) fuzzy systems. The result is based on the so-called fuzzy Lyapunov function, which is used to characterize the subsets of the DA as sublevel sets of the Lyapunov function. The key idea relies on casting the Lyapunov inequality that includes the time-derivative of the membership functions into linear matrix inequalities (LMIs) by considering a bound on the nonlinear function dependent quadratically on the time-derivative of the membership functions. Finally, an example is given to demonstrate the effectiveness of the proposed approach.