In this paper the relationship between state feedback control laws and full information control laws, i.e., control laws which make explicit use of the disturbance signals, is discussed in the framework of nonlinear singular H-infinity control. In particular, it is shown that any (polynomial) full information control law can always be approximated by a state feedback control law, provided that a certain (arbitrarily small) amount of performance is sacrificed. Moreover, the obtained result is used to give alternative proofs and generalizations to some existing results in the area of global disturbance attenuation for nonlinear systems and to establish some new and interesting results regarding the problem of approximate model matching.