  This paper shows that a large class of fading memory state-space systems
driven by discrete-time observations of dynamical systems defined on compact
manifolds always yields continuously differentiable synchronizations. This
general result provides a powerful tool for the representation, reconstruction,
and forecasting of chaotic attractors. It also improves previous statements in
the literature for differentiable generalized synchronizations, whose existence
was so far guaranteed for a restricted family of systems and was detected using
H\"older exponent-based criteria.
