We obtain necessary conditions for the generalised synchronization of coupled dynamical systems, namely the process of confining the dynamics to lower dimensional submanifolds in the phase space. In this framework, synchronization is seen as a process of imposing algebraic constraints which may also be time-dependent. We propose a procedure for constructing (non-unique) coupling functions that can guide the flow to the desired submanifold which can also be made stable and attracting. A geometric analysis of the stability of this manifold is provided, and the procedure is demonstrated through representative examples.