Consensus for Linear Multiagent Systems With Time-Varying Delays: A Frequency Domain Perspective

This paper investigates the consensus problem for multiagent systems with time-varying delays. The bounded delays can be arbitrarily fast time-varying. The communication topology is assumed to be undirected and fixed. With general linear dynamics under average state feedback protocols, the consensus problem is then transformed into the robust control problem. Further, sufficient frequency domain criteria are established in terms of small gain theorem by analyzing the delay dependent gains for both continuous-time and discrete-time systems. The controller synthesis problems can be solved by applying the frequency domain design methods. Numerical examples are demonstrated to verify the effectiveness of the proposed approaches.