Stochastic consensus of linear multi-agent systems: Communication noises and Markovian switching topologies

This paper studies the mean square and almost sure consensus of discrete-time linear multi-agent systems with communication noises under Markovian switching topologies. By a sophisticated stochastic-approximation type protocol, the closed-loop dynamics of this linear multi-agent system can be transformed into a discrete-time first-order integral multi-agent system. It is proved that if all roots of a polynomial, whose coefficients are the parameters in the gain vector of the proposed protocol, are in the unit circle, there is certain equivalence between the consensus of original linear multi-agent system and the consensus of transformed first-order integral multi-agent system. Then some sufficient conditions on the mean square/almost sure consensus of linear multi-agent systems can be obtained accordingly. Finally, theoretical analysis is verified by simulation examples.