For complex dynamical networks with nonlinear different-dimension nodes and coupling functions, a general network model is proposed. For this kind of network, some assumptions are given to achieve its synchronization, and the synchronous definition is presented based on the invariant manifold. Furthermore, decentralized dynamical compensation controllers are synthesized and the synchronization scheme is given. Finally, the synchronous theorem is proved rigorously
by using Lyapunov stability theory, and a numerical example is given to verify the effectiveness of the proposed scheme.