This paper presents the robust control design for aircraft autopilot. The controller provides a maximum stability radius to the closed-loop system. The technique uses the notion of complex stability radius and the Linear Matrix Inequalities (LMI) to obtain the feedback controller gain. The technique is illustrated on a feedback controller of an autopilot system of a twin engine civil aircraft. The results is compared to those that are obtained using a linear quadratic regulator (LQR) technique.