Distributed H∞ coordination of multi-agent systems with directed switching topology and time-delay

In this paper, we consider multi-agent H∞ consensus control problems with external disturbance under directed switching topologies. Both switching networks with and without time-delay are taken into consideration. By the model transformation, the multi-agent H∞ control problem is converted into the switching linear system H∞ control problem with special structure. Based on graph theory and common Lyapunov function method, we establish LMI sufficient conditions under which all agents can reach consensus with the desired H∞ performance in two cases of zero and nonzero communication delays respectively. Specially, we obtain an explicit estimation expression of H∞ performance index in undirected non-time-delay switching topology case. Finally, two numerical examples are provided to illustrate the effectiveness of the obtained results.