In this paper, we present a systematic framework for the design of gain scheduled observer based controllers for affine linear parameter-varying (LPV) systems. Our approach is based on parameter-dependent Lyapunov functions. We give sufficient conditions for the synthesis of the observer gain and of the state feedback controller gain separately and we show that the closed-loop system obtained with the observer based controller is stable. The main contribution of this paper is the fact that the state feedback gain synthesis is formulated as a more easily tractable condition and this is achieved by the application of the multiconvexity concept and the introduction of a slack variable.