This chapter investigates the Takagi-Sugeno modeling approach for nonlinear control and observer design. Several results from the literature based on linear matrix inequalities are summarized and combined to provide a useful control design framework for nonlinear systems. Stability constraints, techniques to include region constraints of the resulting closed-loop dynamics, and robust criteria are discussed and formulated as linear matrix inequalities. A linear matrix inequality constraint for Takagi-Sugeno observers with unmeasurable premise variables based on the input-to-state property is proposed. By combining the presented linear matrix inequalities for the application to a wind turbine, two different nonlinear control schemes based on the convex system description are derived, and the implications from introducing the observer for the wind turbine application are discussed.