Sampled-data based average consensus control for networks of continuous-time integrator agents with measurement noises

In this paper, sampled-data based average-consensus control is considered for networks consisting of continuous-time first-order integrator agents under a noisy distributed communication environment. The impact of the sampling size and the number of network nodes on the system performances is analyzed. The control input of each agent is based only on the information measured at the sampling instants from its neighborhood rather than the complete continuous process, and the measurement of its neighbors states are corrupted by communication noises. By probability limit theory and the property of graph Laplacian, it is shown that for a connected network, when the sampling size is sufficiently small, the static mean square error between the individual state and the average initial states of all nodes is arbitrarily small. Furthermore, by choosing properly the consensus gains the almost sure consensus can be achieved. It is worth pointing out that an uncertainty principle of Gaussian networks is obtained, which tells us that in the case of white Gaussian noises, no matter what the sampling size is, the product of the static and transient performance indexes is always equal to or larger than a constant depending on the noise intensity, network topology and the number of network nodes.