The critical delay of the consensus for a class of multi-agent system involving task strategies

The time delay may induce oscillatory behaviour in multi-agent systems, which may destroy the consensus of the system. Therefore, the critical delay that is the maximum value of the delay to guarantee the consensus of the system, is an important performance index of multi-agent systems. This paper studies the influence of the processing delay on the consensus for a class of multi-agent system involving task strategies. The first-order system with a single delay and the second-order system with two different delays are investigated respectively. A critical delay independent of strategies and a critical region of the 2-D plane that depends on strategies is obtained for the first-order and the second-order system respectively. Specifically, a geometric method was used for the case of two different delays. Several numerical simulations are presented to explain the results.