On constructing Lyapunov function for formation control of Multi-agent Systems with directed topology

This paper considers the time-varying formation problem for Multi-agent Systems, which the communication topology is directed. Distributed consensus protocol is constructed based on relative states information of neighbor agents. Then using the full rank decomposition of the Laplacian matrix, one linear transformation is introduced to transform the formation problem into consensus problem. By constructing a proper formation error vector, the formation problem with directed topology is converted into a stabilization problem of a reduced dimensionality error system. Sufficient conditions are obtained using Lyapunov approach. The new approach can relax the constraint of topology condition. Finally, numerical simulations are provided to demonstrate the effectiveness of the analytical results.