This paper develops a robust H controller for a pitching and plunging airfoil using the state space representation of Theodorsen's lift model employing the linear matrix inequalities method. Both parameter uncertainty and the input disturbances are considered in the model. The existence condition for the robust H state-feedback controller is obtained using the Lyapunov functional approach. In practical systems, it is difficult to obtain all the states of the model needed for the controller. Thus, the observer existence condition is proposed to provide the states' information for the model. Several examples are used to demonstrate the effectiveness of the designed controller and the designed observer.