Delayed state synchronization of continuous-time multi-agent systems in the presence of unknown communication delays (including complete proofs)

This paper studies delayed synchronization of continuous-time multi-agent systems (MAS) in the presence of unknown nonuniform communication delays. A delay-free transformation is developed based on a communication network which is a directed spanning tree, which can transform the original MAS to a new one without delays. By using this transformation, we design a static protocol for full-state coupling and a dynamic protocol for delayed state synchronization for homogeneous MAS via full- and partial-state coupling. Meanwhile, the delayed output synchronization is also studied for heterogeneous MAS, which is achieved by using a low-gain and output regulation based dynamic protocol design via the delay-free transformation.