Consensus of discrete-time second-order multi-agent systems with delayed and noisy measurements under balanced digraphs

This paper studies mean square and almost sure consensus of discrete-time second-order multi-agent systems with time-delays and multiplicative noises in the information exchange with neighbors. By using the stochastic stability theorem of discrete-time stochastic delay systems, we find sufficient conditions for mean square and almost sure consensus explicitly related to the network and control parameters. It is shown that if the network graph is balanced and strongly connected, then the weighted-average type control protocol can be properly designed to ensure mean square and almost sure consensus for any given time-delays and noise intensity coefficients.