The existence of three types of generalized synchronization of unidirectionally coupled non-autonomous systems is studied. When the modified response system collapses to an asymptotically stable equilibrium, asymptotically stable periodic or quasi-periodic orbits, under certain conditions, the existence of generalized synchronization can be turned to the problem of compression fixed point in the family of Lipschitz functions. Theoretical proofs are proposed to the exponential attractive property of generalized synchronization manifold. In addition, the Duffing system was taken for illustration and verification.