Necessary and Sufficient Consensus Conditions of Descriptor Multi-agent Systems

For descriptor multi-agent systems with fixed topology and agents described by general descriptor linear time-invariant systems, necessary and sufficient conditions of consensusability with respect to a set of admissible consensus protocols are proposed using the tools of algebra, graph and descriptor linear system theory. The consensusability conditions depend on both the structure properties of each agent´s dynamics and the topology within the descriptor multi-agent systems. Designing an output feedback control law can guarantee that the studied descriptor multi-agent system is consensusable with respect to a given admissible set. A provided example indicates the applicability of the proposed approach.