Robust Consensus for Linear Multi-Agent Systems over Randomly Switching Topologies

This paper investigates the robust mean square consensus problem for linear discrete-time multi-agent systems over arbitrarily switching topologies with unknown transition probabilities. The switching is governed by a time-homogeneous Markov process from a set of possible interaction topologies among agents. A sufficient condition is proposed for achieving mean-square consensus under a common control protocol. Moreover, the solution of the controller is formulated as a group of LMI constraints. Finally, the theoretical results are validated via a numerical simulation example.