Mean square consensus control for second order multi-agent systems under fixed topologies and measurement noises

This paper considers the mean square consensus problems for second order multi-agent systems with fixed topologies and measurement noises. Two cases were analyzed: 1) undirected networks with fixed topologies; 2) undirected networks with fixed topologies and measurement noises. In order to attenuate the measurement noises, a time-varying consensus gain was introduced in the consensus protocol. Sufficient conditions were derived for all agents to reach consensus in mean square via algebraic graph theory, matrix theory and stochastic analysis approach, by constructing an appropriate Lyapunov function. A numerical example was given to verify our theoretical analysis