Consensus Performance of First-Order Agents
Yanling Ding, Hui Peng, Tian Qi, Jie Chen · IEEE Transactions on Automatic Control · 2024
This paper concerns consensus problems of linear time-invariant systems with stochastic noises and deterministic disturbances. We consider first-order dynamic agents interconnected by a directed graph network subject to inter-agent time delay, and we seek to determine the error performance achievable by consensus feedback protocol, whereas the performance quantifies the disruption of consensus by noises and disturbances. The$\mathcal {H}_{2}$and$\mathcal {H}_\infty$norms of the multi-agent system transfer function matrices are employed as measures of the consensus error. For the$\mathcal {H}_{2}$consensus performance, we obtain an analytical expression of the consensus error, while for the$\mathcal {H}_\infty$consensus performance, we show that it can be determined by solving a sequence of independent unimodal quasi-convex problems. The results help demonstrate how in the presence of stochastic noises and deterministic disturbances the agent's unstable dynamics may interact over a delayed network to limit the consensus performance attainable.