Generalized states, the state representations of which depend on time derivatives of the input, are naturally used in the control design for fiat systems. Quasi-static feedback of these generalized states, which involves time derivatives of the closed-loop input, is shown to allow control of all flat systems by feedback linearization of the tracking error dynamics. This is then used in a method proposed for the analysis and design by subsystems of certain flat series connections. The results are illustrated on a gantry crane example.