The Unmanned Aerial Vehicles (UAVs) have recently proven to be of immense help in both military and civilian fields. All UAVs ideally need to be able to operate at runtime without the need for sustained human supervision. Hence, the role of automatic control and in particular optimal control of UAVs cannot be overemphasized. In this paper, an eighth-order, non-linear model of a typical UAV is considered. The linearized model of the system exhibits time-scale (slow and fast) character. Based on the time-scale separation, analysis and design of the UAV is carried out successfully by first separating the original, high-order system into slow and fast, lower-order subsystems. Then optimal controllers for these subsystems are designed and a composite control is formed from the slow and fast controls for both deterministic and stochastic cases. The simulations show good agreement between the original linear system and the slow and fast subsystems.