Interval Type-2 (IT2) fuzzy systems have gained significant attention due to their strong capability in handling system uncertainties. This paper investigates the robust stability analysis of conventional Takagi–Sugeno (TS) IT2 fuzzy systems under an observer-based control framework. A non-uniform piecewise linear approximation method is introduced to more accurately capture the boundary characteristics of IT2 membership functions (MFs), allowing key variation information of MFs to be effectively exploited. Subsequently, an error model transformation strategy is proposed to reconstruct approximation-induced errors into an auxiliary fuzzy model, enabling richer error-related and MF information to be explicitly incorporated into the stability conditions and thereby reducing conservatism. By leveraging Lyapunov stability theory and a scaling approach, sufficient stability criteria are derived in terms of linear matrix inequalities (LMIs), which can be efficiently solved using standard convex optimization tools. Simulation results and comparative studies demonstrate that the proposed method achieves less conservative stability conditions and enhanced robustness compared with existing approaches.
Yang et al. (2026) studied this question.