Robustness analysis of leader-follower consensus

In this paper, the robustness of the leader-follower consensus is considered in the presence of communication errors. For simplicity of the presentation, the problem is restricted to a time-invariant communication topology when each node apart from the leader has in-degree 1. Two different robustness measures are considered: the L₂ gain of the error vector to the state of the network and the worst case L₂ gain at the node. Simulation results and theoretical analysis show that the worst case L₂ gain of the node highly depends on the communication topology and is less sensitive to the number of the nodes. We show that when the leader can communicate to each node in the network, both two measures reach their minimal values.