We develop a robust fault detection and isolation (FDI) technique in the presence of measurement noise and apply it to the horizontal axis variable speed wind turbine. In the first part, we provide a nonlinear model of the wind turbine in the form of differential-algebraic equations. We consider wind as a disturbance to the system, having two components: The wind speed and the wind direction. In the second part, treating the nonlinear term due to wind in the system dynamics as an unknown disturbance, we propose an optimization-based approach to robustify a linear residual generator with respect to measurement noise. The contribution of the noise into the residual is introduced in the framework of linear matrix inequalities, in which the requirements of the FDI filter are modeled as linear constraints. We illustrate the performance of our proposed method on the wind turbine benchmark model implemented in the FAST simulation code. © 2013 AACC American Automatic Control Council.