Owing to the aerodynamic conversion process, wind turbines exhibit a nonlinear behavior and encounter turbulent operating conditions that demand well-defined closed-loop dynamics to withstand accumulated loading over the lifetime. Wind excitation is the main disturbance and driving force for the system and determines the necessary operating strategy, but it usually represents an unmeasurable quantity. In this study, we used a linear-matrix-inequalities-based control and observer design to operate a variable-speed, variable-pitch wind turbine in a wind tunnel experiment at different reproducible inflow conditions while relying on a wind speed estimate obtained from a disturbance observer. The computational complexity of the stability framework incorporating the reconstruction of the unknown wind speed is reduced by exploiting characteristics of the modeling approach based on a convex combination of linear submodels. The assumption used in the proposed stability consideration is evaluated based on measurement data. We introduced an extended operating range compared to the commonly considered operating trajectory of wind turbines in the control design. A controller based on Takagi–Sugeno modeling is used to operate the turbine at challenging power tracking requirements demonstrating the capability to support fast stabilization of the electrical grid while discussing the loading and operational constraints observed during the experiments.