An iterative redesign algorithm is proposed to integrate the design of the structural parameters and a linear parameter varying (LPV) controller for a wind turbine. The LPV controller is designed for a lumped model of the wind turbine with five degrees-of-freedom consisting of blades, drivetrain and the tower. The controller is scheduled in real-time based on the mean wind speed. The controller objective is to track an optimal power generation trajectory and minimize the H∞ performance index from the wind turbulence disturbance to the controlled output vector. The solution of the problem is formulated as an iterative sequential controller/structure redesign to obtain the values corresponding to a local optimal performance index. Each step of the iterative procedure is formulated as a linear matrix inequality (LMI) optimization problem that can be solved efficiently using available LMI solvers. The simulation results show the effectiveness of the algorithm in converging to a local optimal solution and improving the overall performance of the system in FAST closed-loop responses via the integrated design.