\begin{document}$H_\infty$\end{document} Consensus Control of Discrete-Time Multi-Agent Systems Under Network Imperfections and External Disturbance

This paper presents a distributed control protocol for consensus control of multi-agent systems (MASs) under external disturbances and network imperfections, including communication delay and random packet dropout. To comply with the discrete nature of networked systems, in contrast to most of the existing work for MASs under network imperfections, the agents are modeled by discrete-time dynamics. The communication network is considered to be undirected, its delay is considered to be time-varying but bounded, and its packet dropout is modeled by a Bernoulli distributed white sequence. Sufficient conditions in terms of linear matrix inequalities (LMIs) for asymptotic mean-square consensus stability are derived under network imperfections without considering external disturbances. A desired disturbance attenuation level in the presence of both external disturbances and network imperfections is also provided. A simulation example is given to verify the effectiveness of the proposed approach in coping with network imperfection and disturbances.