Formation control synthesis in local frames under communication delays and switching topology: An LMI approach

This paper presents a formation control synthesis method for a multiagent system to reach a prescribed rigid formation under communication delays and time-varying switching communication topology. The proposed control scheme only requires the knowledge of relative measurements of some neighbor agents, expressed in each agent's local frame, to be implemented. The presence of communication delays and switching topology are critical factors in the control design that could lead the system to slow convergence or even instability. To cope with this problem, we give sufficient conditions based on Linear Matrix Inequalities (LMI) and convex sum relaxation techniques which allow finding the control parameters that maximize the worst-case delay whilst keeping a minimum speed of convergence. Finally, simulation results are provided to show the effectiveness of the proposed approach.