  Robust time-varying formation design problems for second-order multi-agent
systems subjected to external disturbances are investigated. Firstly, by
constructing an extended state observer, the disturbance compensation is
estimated, which is a critical term in the proposed robust time-varying
formation control protocol. Then, an explicit expression of the formation
center function is determined and impacts of disturbance compensations on the
formation center function are presented. With the formation feasibility
conditions, robust time-varying formation design criteria are derived to
determine the gain matrix of the formation control protocol by utilizing the
algebraic Riccati equation technique. Furthermore, the tracking performance and
the robustness property of multi-agent systems are analyzed. Finally, the
numerical simulation is provided to illustrate the effectiveness of theoretical
results.
