Disturbance observer-based consensus control of input-delayed LTI systems with matched disturbances: a predictor feedback approach

The study addresses the consensus problem of linear time invariant (LTI) multi-agent systems with constant input delay and matched external disturbances by using relative output information. First, distributed disturbance observers are constructed to estimate the disturbances generated by linear exosystems with unknown initial conditions. Next, a disturbance observer-based predictor feedback control law is developed for each agent to realise consensus disturbance rejection in the presence of input delay. Then, a linear matrix inequality-based control design algorithm is given to determine the satisfactory control parameters. It is proved that state consensus can be achieved for both leaderless and leader-follower networks in the presence of large input delay and matched disturbances under the control scheme. Finally, a simulation example is provided to validate the theoretical results.