In this paper, a robust autopilot is proposed using stable interpolation based on Youla parameterization. The most important condition of stable interpolation between local controllers is the preservation of stability so that each local controller can ensure stability for an open neighborhood around a nominal point. The proposed design used fixed-order robust controller with parameter-dependent central polynomial for each vertex of the polytope to decrease the conservation of each local controller. A stability-preserving gain-scheduled controller was designed using a newly proposed algorithm in the flight envelop for a parameter varying model. The results of simulation confirm the efficiency of the proposed method.