Leader-follower Consensus in Undirected Communication Networks With Directed Links to the Leader

This study analyzes a consensus problem for multi-node systems structured as leader-follower communication networks, aiming to achieve agreement among all nodes in a network. The main network, which consists of follower nodes, is undirected, and directed connections from follower nodes to a leader node are added to the main network structure. The weights defined in the main network can be either positive or negative. The consensus algorithm proposed in this paper requires each follower node to use only local information, ensuring a fully distributed implementation. Numerical analysis reveals that all follower nodes converge to a desired value provided by the leader node when the desired value remains constant. In contrast, in the case where the desired value changes continuously, all follower nodes are shown to remain bounded within a neighborhood of the leader. Simulation results are presented to validate our theoretical findings.