A multi-agent system like a network of automotive vehicles could collectively perform a complex task beyond their individual capabilities. This research focuses on the control of multi-agent system formation by controlling relative inter-agent distance. The kinematic system formation model is represented by a rigid graph and the controller is designed by using Lyapunov stability theory. And formation tasks, formation acquisition, formation maneuvering and target interception, are the main problems discussed in this research. What's more, the research could extend from static formation to dynamic formation, from single-integrator agent model to double-integrator one and from dual direction inter-agent control to single direction one.