Interval Observer Design for Discrete-Time Uncertain Takagi–Sugeno Fuzzy Systems

Abstract

This paper proposes a novel interval observer design method for discrete-time Takagi–Sugeno fuzzy systems with parametric uncertainty, disturbances, and measurement noise. We present a new structure of interval observer with more design parameters, which can be used to broaden the application scope of interval observer design. For improving the accuracy of interval estimation, an $L_{\\infty }$ norm-based approach is used in the design of interval observer to attenuate the effect of the unknown disturbances, noise, and parametric uncertainty. Furthermore, the design conditions are formulated into a set of linear matrix inequalities, which can be efficiently solved. Numerical simulations are given to illustrate the effectiveness of the proposed method.