The paper is devoted to the problem of designing robust unknown input observer (UIO) for fault estimation purpose. The proposed approach is based on the Takagi-Sugeno models which can be effectively applied for modelling of the wide class of non-linear systems. It also revisits the recent results proposed in the literature and provides a less restrictive design procedure of a robust UIO. In particular, the general UIO strategy and the H1 framework are provided to design a robust fault estimation methodology. The resulting design procedure guarantees that a prescribed disturbance attenuation level is achieved with respect to the state estimation error. The main advantage of the proposed approach boils down to its simplicity because it reduces to solving a set of Linear Matrix Inequalities (LMIs). The final part of the paper presents an illustrative example devoted to the fault estimation of a three blade 1 MW variable-speed, variable-pitch wind turbine.