On time-varying formation feasibility and reference function of time-delayed linear multiagent systems with switching digraphs

Time-varying formation feasibility and formation reference function of linear multiagent systems with both time-varying delays and switching directed topologies are studied. For a given linear multiagent system, not all the time-varying formations can be realized due to the dynamic restriction of each agent. The formation feasibility constraint reveals the requirement on the desired time-varying formation to be compatible with the agent dynamics. Formation reference is a representation for the macroscopic movement of the whole multiagent system. Novel features of the formation feasibility constraint and the formation reference are the main focus of this paper. Firstly, a time-delayed formation control protocol with switching directed topologies is constructed using local neighboring information. Then, a time-varying formation feasibility constraint is derived based on nonsingular transformations. It is proven that the time-varying formation feasibility constraint is independent of the time-varying delays and the switching directed topologies. Moreover, an explicit expression of the formation reference function is proposed. It is shown that neither the time-varying delays nor the switching directed topologies has influence on the obtained formation reference function. Finally, comparative examples are provided to demonstrate the obtained results.