State Interval Estimation Method for N-TS Fuzzy Model with Membership Function-Dependent L_∞ Performance

To address the high computational complexity caused by the excessive number of rules in traditional Takagi-Sugeno fuzzy models for complex nonlinear systems, this paper proposes a state interval estimation method based on an N-TS fuzzy model. By employing nonlinear partitioning techniques to eliminate dependence on unmeasurable antecedent variables, the number of fuzzy rules is significantly reduced, thereby lowering real-time computational burdens. Furthermore, a membership function-dependent L<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> performance index is designed to optimize disturbance rejection constraints for individual fuzzy rules through a dynamic weighting mechanism. This approach overcomes the conservatism of traditional global time-invariant performance metrics, enhances system robustness, and generates tighter ellipsoidal interval bounds. Based on Lyapunov stability theory and the linear matrix inequality (LMI) framework, observer gain design conditions are derived, rigorously proving the asymptotic stability of the error system and the feasibility of the L<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> performance. Simulation results demonstrate that, compared to conventional methods, the proposed approach achieves tighter interval estimations while maintaining state estimation accuracy.