Zs. Lendek, J. Lauber, T.M. Guerra, R. Babuska, and B. De Schutter, "Adaptive observers for TS fuzzy systems with unknown polynomial inputs," Fuzzy Sets and Systems, vol. 161, no. 15, pp. 2043-2065, Aug. 2010.
A large class of nonlinear systems can be well approximated by Takagi-Sugeno (TS) fuzzy models, with linear or affine consequents. However, in practical applications, the process under consideration may be affected by unknown inputs, such as disturbances, faults or unmodeled dynamics. In this paper, we consider the problem of simultaneously estimating the state and unknown inputs in TS systems. The inputs considered in this paper are 1) polynomials in time (such as a bias in the model or an unknown ramp input acting on the model) and 2) unmodeled dynamics. The proposed observer is designed based on the known part of the fuzzy model. Conditions on the asymptotic convergence of the observer are presented and the design guarantees an ultimate bound on the error signal. The results are illustrated on a simulation example.