A Performance-Region-Based Approach to the H ∞ Stochastic Consensus Problem

This brief considers the H∞consensus problem of networked general linear agents subject to external disturbances over Markovian randomly switching communication topologies. To solve this problem, a class of observer-based consensus control protocols is proposed, which solely depend on the local information of each agent. Under the proposed protocol, it is interesting to find that the H∞stochastic consensus problem of the multi-agent system can be cast into the H∞robust control problems of some independent systems with the same dimension as a single agent. For the purpose of designing the proposed protocol, the notion of H∞consensus performance region is first introduced and then analysed. Based on the theoretical analysis, an algorithm is given to solve the H∞stochastic consensus problem. Finally, it is pointed out via some numerical simulations that a small enough positive coupling strength can make the consensus protocol be robust to the variations of the communication topology.