We investigate the cooperative control and global asymptotic synchronization Lagrangian system groups, such as industrial robots. The proposed control approach works to accomplish multirobot systems synchronization under an undirected connected communication topology. The control strategy is to synchronize each robot in position and velocity to others robots in the network with respect to the common desired trajectory. The cooperative robot network only requires local neighbor-to-neighbor information exchange between manipulators and does not assume the existence of an explicit leader in the team. It is assumed that network robots have the same number of joints and equivalent joint work spaces. A combination of the lyapunov-based technique and the cross-coupling method has been used to establish the multirobot system asymptotic stability. The developed control combines trajectory tracking and coordination algorithms. To address the time-delay problem in the cooperative network communication, the suggested synchronization control law is shown to synchronize multiple robots as well as to track given trajectory, taking into account the presence of the time delay. To this end, Krasovskii functional method has been used to deal with the delay-dependent stability problem.