||This talk first presents a novel approach to establish synchronization of coupled systems. Then, we establish the global synchronization of a network of linearly coupled systems based on this approach. Under the present framework, the coupling configuration of the coupled systems can be quite general. The connection matrices are free from the commonly imposed conditions and can be time-dependent, asymmetric, with nonzero row-sums or non-positive off-diagonal entries. We apply the derived synchronization criterion to study the global synchronization of coupled Lorenz equations. We first establish the dissipative property of coupled Lorenz equations. From this property, we derive a criterion for the global synchronization of Lorenz equations under general coupling scheme. The criterion can be expressed transparently and examined by straightforward computations. For non-diffusively coupled Lorenz equations, we show that the chaotic behavior can emerge, or conversely, be suppressed, as the coupled equations synchronize under the synchronization criterion.