Analysis of ${H}_{\infty }$ 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.