Abstract
In this paper, we investigate the leaderless bipartite synchronization problem about nonlinear systems with time delay under Markov switching topologies. We first deal with the strongly connected part of the coupled system. Then, by utilizing the consensus trajectory of the strongly connected agents, we transform the consensus problem into a stable problem. A mild condition about switching topology is proposed which just require the union graph has a spanning tree. We also propose a novel method to deal with the error system. Then, sufficient conditions are presented to make all the systems achieve bipartite synchronization under ergodic Makrov switching topology. At last, an example is given to verify our theory.
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