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This paper deals with a computational optimization approach to the problem of state-feedback control design for a wind turbine system. The first step of the study is to develop a reduced order model for the system by considering the most important physical phenomena of aerodynamics and structural dynamics. Moreover, the behavior of the system can be influenced by the coupled dynamics between the tower motions and the blade pitch and turbine speed which can cause instabilities in the control loops in the worst case. By using a suitable wavelet function, called Haar functions, a recursive computational procedure is established for finding the system dynamics approximately by solving only algebraic equations instead of solving the Riccati differential. Simulation results are given to illustrate the usefulness of the proposed control methodology.