Stochastic averaging approach to leader-following consensus of linear multi-agent systems

Recently, consensus of high-order linear multi-agent systems (MAS) has received much attention by many researchers, putting emphasis mainly on dealing with fixed network topology, with relatively few attention on the case of switching topology. The averaging method proposed in Ni et al. (2012, 2013) [26,27] was shown to be a powerful tool to investigate consensus problem of deterministic switching high-order MAS. This paper aims at extending the deterministic averaging method to the stochastic case which includes communication white noises and Markovian switching network topology, where the commonly used assumptions in existing literature on the decreasing gain and the balance of the underlying graph were abandoned. The stochastic averaging based method can tackle the challenge problem of investigating the joint effect of the stochastic network topology, the high-order dynamics of the agents and the noisy communication among agents on the consensus. Extension to observer-based leader-following consensus is also explored and stochastic version of separation principle is obtained.