Consensus for general multi-agent systems over random graphs

This paper studies the consensusability problem for general multi-agent systems over random graphs. Two types of consensusability notions, namely mean square consensusability and probabilistic consensusability, are examined. We first consider a graph model with Markovian switching topologies for continuous-time agent dynamic. For the counterpart of discrete-time case, we consider the graph model with random link failures. Sufficient conditions are derived for both consensusability notions, which reveal how Markovian switchings and random link failures affect consensusability. Our results can naturally recover the existing literature on fixed topologies.