This chapter proposes observer-based control of FASs with partial state feedback, both full-order observers and reduced-order observers are considered. For full-order observer-based control, a dynamical output feedback control scheme consists of a full-order observer and a feedback controller with full-actuation property is proposed for a FAS satisfying Lipschitz assumption. For reduced-order observer-based control, a dynamical output feedback controller is also proposed based on a reduced-order observer for a FAS satisfying partial Lipschitz assumption, both general and special cases are discussed. For both designs, the closed-loop stability is proven, particularly with the observation errors converging to zero. Illustrative examples demonstrate the solution procedure and the effect of the proposed FAS approaches.