Interval Estimation for Discrete-Time Takagi–Sugeno Fuzzy Nonlinear Systems With Parameter Uncertainties

This article proposes a two-step interval estimation method for discrete-time Takagi–Sugeno fuzzy nonlinear systems with parameter uncertainties. First, a novel observer structure without redundant parameters is proposed to obtain point-valued estimation for the considered system. Compared with the $T$–$N$–$L$ observer structure recently presented in the literature, the proposed observer structure is more concise and can simplify the design process. To improve the estimation accuracy, an $H_\infty$ design method that can simultaneously optimize all design parameters by solving linear matrix inequalities is proposed to design the proposed observer. Second, interval estimation is achieved by zonotopic analysis on the error dynamics of the designed observer. Comparison studies show that the proposed method not only has broader application scopes but also can obtain more accurate estimation results than a state-of-the-art interval observer design method. Moreover, the proposed method is applied to a missile control system to estimate the intervals of the attack angle and pitch rate.