This brief studies the distributed consensus problem for multiple nonidentical matching nonlinear systems. In fully distributed fashion, a class of edge-based protocols with adaptive coupling strengths is proposed. By using a combined tool from nonsmooth control theory and matrix analysis, it is proved that the states of the agents equipped with the designed protocols will achieve consensus under an arbitrarily given connected topology. A remarkable feature of this approach is that the final consensus value of the closed-loop multiagent systems is analytically derived when there is no external disturbance.