Consensus Analysis of Fractional Multi-Agent Systems with Delayed Distributed PI Controller

The consensus problem for fractional multi-agent systems (MASs) with time delay is considered. The distributed fractional proportional-integral (PI)-type controller is designed so that the consensus of the proposed systems is achieved. Moreover, explicit condition to determine the crossing directions is developed. The results show that with the increase of time delay, the closed-loop system has two different dynamic characteristics: From consensus to nonconsensus and consensus switching. Furthermore, delay margin within which consensus of MASs will always hold is determined. The results should provide useful guidelines in the consensus analysis and in the analytical design of the distributed controllers.