Consensus problems of high-order swarm system over random topologies with time-varying communication probability are investigated. Firstly, based on the random relative information of neighboring agents, distributed dynamic consensus protocols are proposed. Then, by using the state space decomposition approach to analyze discrete-time highorder multi-agent network, a necessary and sufficient condition for consensus over random topologies with probability 1 is
given. Moreover, the explicit expression of the consensus function is presented via random topologies. Finally, numerical simulations demonstrate the correctness of the obtained theoretical results.