The invariant ellipsoid methodology focuses on minimizing the invariant/attractive set for a linear control system subjects to bounded external disturbances. In this note, the invariant ellipsoid methodology is adapted to multiagent systems (MASs) by leveraging the generalized homogeneous control. A necessary and sufficient condition for the optimal rejection of external disturbances using a homogeneous control protocol is presented. Compared to linear control protocols, the generalized homogeneous approach yields faster convergence and enhanced accuracy. Theoretical results are validated by the numerical simulations of the multiagent system comprised of unicycle mobile robots (UMRs).

A novel scheme for an "upgrade" of a linear control algorithm to a non-linear one is developed based on the concepts of a generalized homogeneity and an implicit homogeneous feedback design. Some tuning rules for a guaranteed improvement of a regulation quality are proposed. Theoretical results are confirmed by real experiments with the quadrotor QDrone of Quanser™.