Abstract: The LPV (Linear Parameter-Varying) system of turbofan engine was put into apolytopic expression by a convex decomposition,and the polytopic features were used to simplifythe controller design to a vertices' controller design.By using a LMI (Linear Matrix Inequality)approach,a feedback controller with the pole placement in a given region and with unique Lya-punov function for every vertex was designed, which satisfied H∞performance requirement.Aglobal continuous gain scheduled controller was then obtained by the synthesis of the vertex con-trollers.As compared with PID controller, the designed controller demonstrates its feasibility.