Abstract: In consideration of the extreme flexibility characteristics of film sail and large-scale booms of solar sail, a nonlinear rigid-flexible coupling dynamic model is presented. Under some assumptions, the model is translated into a polytopic linear parameter-varying (LPV) system, and then a state feedback control law is designed for the polytopic LPV system. Solutions of the parameters of the controller are obtained by solving the convex optimization problem with linear matrix inequality (LMI) constraints. Finally the simulation results show that the proposed method is effective, as the asymptotic tracking of the sail target attitude angle and robust vibration suppression of flexible structures are all achieved.