This paper proposes a computationally efficient and traceable way to synthesize finite horizon linear time-varying (LTV) output feedback controllers. It is based on a separate observer and state feedback synthesis with guaranteed performance in a mixed sensitivity setting. The approach avoids a grid-wise evaluation of coupled synthesis conditions that limits existing output feedback syntheses and instead uses two subsequent steps. However, it guarantees the same performance as the original output feedback problem. A trajectory tracking controller for an ascending space launcher in the earth’s atmosphere demonstrates the feasibility of the approach.