This paper presents a novel approach to robust linear time-varying control design for space launchers. It allows the controller to explicitly account for the launcher’s time-varying dynamics and changing control objectives along the ascent trajectory. The latter are readily incorporated via time-varying weighting functions into a mixed sensitivity design. For a traceable and transparent control design, a physically motivated weighting scheme is applied, which requires little tuning effort. The controller is obtained via a novel observer-based finite horizon linear time-varying synthesis approach. It provides a transparent structure which is easy to implement. The approach is used to design a pitch controller for a flexible expendable launch vehicle in atmospheric ascent tracking the open-loop guidance reference signal.