Root Locus Design for the Synchronization of Multi-Agent Systems in General Directed Networks∗

This paper considers the synchronization problem of multi-agent SISO systems with general unidirectional communication structures. A distributed control strategy is presented which relies on relative output differences of neighboring agents and, thus, does not need relative state information. We propose a root locus design method to determine the synchronization gain. Since in directed networks the characteristic equation for synchronization might be complex valued, we use tools from the complex root locus technique to solve the synchronization task.