Consensus Control of Second-Order Stochastic Delayed Multi-Agent Systems with Intrinsic Dynamics and Undirected Topologies

Abstract In this paper, we address the consensus control of stochastic multi-agent systems with intrinsic dynamics based on measurements with time-delay and multiplicative noises under undirected graphs. By developing degenerate Lyapunov functional and stochastic stability theorem, we establish mean square and almost sure consensus conditions explicitly related to the nonlinearity of agent dynamics, control gains, noise intensities and parameters of network graphs. Especially, for the case with linear dynamics, we get necessary conditions for mean square consensus. It is shown that with respect to the weighted-average type control protocols, second-order multi-agent systems are kept mean square consentable with multiplicative measurement noises alone or intrinsic dynamics alone, but may become unconsentable due to the co-existence of multiplicative noises and intrinsic dynamics.