Analysis of Performance for Multiagent Networks

In this article, we analyze the {H}_{\infty } performance of the first-order continuous-time multiagent consensus network and that of the corresponding sampled-data network in the presence of external disturbances. First, we build the quantitative relation between the {H}_{\infty } performance and the eigenvalues of directed graph Laplacian for the continuous-time multiagent network. Second, we establish the analytic expression of {H}_{\infty } performance for the sampled-data multiagent network, which depends not only on the eigenvalues of the Laplacian matrix but also on the sampling period. It is proved that there exists a unique optimal sampling period such that the sampled-data multiagent network obtains the optimal {H}_{\infty } performance. Furthermore, we show that the {H}_{\infty } performance of the sampled-data multiagent network is not better than that of the original continuous-time multiagent network. Finally, numerical tests are given on several well-known graphs.