Analysis of ${H}_{\infty }$ Performance for Multiagent Networks
Jiamin Wang, Jian Liu, Yuanshi Zheng, Jianxiang Xi · IEEE Transactions on Automatic Control · 2023
In this paper, we analyze the${H}_{\infty }$performance of the first-order continuous-time multi-agent consensus network and that of the corresponding sampled-data network in the presence of external disturbances. Firstly, we build the quantitative relation between the${H}_{\infty }$performance and the eigenvalues of directed graph Laplacian for the continuous-time multi-agent network. Secondly, we establish the analytic expression of${H}_{\infty }$performance for the sampled-data multi-agent network, which depends not only the eigenvalues of Laplacian matrix but also the sampling period. It is proved that there exists a unique optimal sampling period such that the sampled-data multi-agent network obtains the optimal${H}_{\infty }$performance. Furthermore, we show that the${H}_{\infty }$performance of the sampled-data multi-agent network is not better than that of the original continuous-time multi-agent network. Finally, numerical tests are given on several well-known graphs.