Aperiodic Sampled-Data Takagi–Sugeno Fuzzy Extended State Observer for a Class of Uncertain Nonlinear Systems With External Disturbance and Unmodeled Dynamics

Abstract

For the extended state observer (ESO) design, the most challenging issue is to exploit efficient nonlinear observation performance, while maintaining desirable linear numerical tractability under noncontinuous transmission. In this article, in order to address this issue, the sampled-data ESO design is investigated for a class of uncertain nonlinear systems. First, based on the fuzzy modeling approach with reasonable fuzzy rules and sets, the nonlinear functions of the ESO are suitably approximated by several local linear models weighted by membership functions. Then, a novel methodology of Takagi–Sugeno fuzzy extended state observer (TSFESO) is developed for the first time. By virtue of fuzzy membership functions, the estimating action is implemented in a nonlinear pattern, while taking advantages of Takagi–Sugeno fuzzy formulation, the observer gains can be calculated in a linear manner. As a result, the nonlinear estimating efficiency and linear numerical tractability are integrated in a unified framework. Second, for the aperiodic sampling case, the exponential convergence criterion for the TSFESO is presented by constructing a sampling- and time-dependent Lyapunov functional, in which the information on sampling action is taken into full consideration for desirable feasibility. Moreover, the observer design approach is also put forward. Finally, the superiorities and effectiveness of the proposed approaches are demonstrated by numerical examples.