Abstract
This technical correspondence studies the consensus problem for second-order multiagent systems under network topologies with a directed spanning tree. Consensus analysis for systems with the distributed delayed proportional-integral (PI)-type controller is given. Crossing directions of the characteristic roots can be identified by a sufficient condition. If the rightward crossing condition holds, the delay margin can be obtained to guarantee that the systems reach consensus if and only if the time delay is less than the critical value. Otherwise, it is possible that the systems switch from consensus to nonconsensus and back to the consensus as the delay increases. Simulation examples are provided to demonstrate the theoretical analysis.
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