Consensus of descriptor multi-agent systems via dynamic compensators

This study deals with the consensus problem via dynamic output feedback (dynamic compensator) for descriptor (singular) multi-agent systems with fixed topologies and agents described by general linear systems. Only output information of each agent can be delivered from its neighbour agents. Based on graph, algebra and descriptor linear system theory, the necessary and sufficient conditions are proposed for the existence of dynamic compensators solving the considered problem. The given conditions depend on both the topologies within descriptor multi-agent systems and the structure properties of each agent dynamics. According to non-zero eigenvalues of the Laplacian matrix of the weighted digraph are the same or different, two consensus algorithms via dynamic compensators are proposed, respectively. The provided examples demonstrate the effectiveness of the proposed consensus algorithms.